A Deep Learning Framework for Heat Demand Forecasting using Time-Frequency Representations of Decomposed Features

Adithya Ramachandran; Satyaki Chatterjee; Thorkil Flensmark B. Neergaard; Maximilian Oberndoerfer; Andreas Maier; Siming Bayer

cs.LGMar 1, 2026

A Deep Learning Framework for Heat Demand Forecasting using Time-Frequency Representations of Decomposed Features

Authors: Adithya Ramachandran, Satyaki Chatterjee, Thorkil Flensmark B. Neergaard, Maximilian Oberndoerfer, Andreas Maier, Siming Bayer

Abstract

District Heating Systems are essential infrastructure for delivering heat to consumers across a geographic region sustainably, yet efficient management relies on optimizing diverse energy sources, such as wood, gas, electricity, and solar, in response to fluctuating demand. Aligning supply with demand is critical not only for ensuring reliable heat distribution but also for minimizing carbon emissions and extending infrastructure lifespan through lower operating temperatures. However, accurate multi-step forecasting to support these goals remains challenging due to complex, non-linear usage patterns and external dependencies. In this work, we propose a novel deep learning framework for day-ahead heat demand prediction that leverages time-frequency representations of historical data. By applying Continuous Wavelet Transform to decomposed demand and external meteorological factors, our approach enables Convolutional Neural Networks to learn hierarchical temporal features that are often inaccessible to standard time domain models. We systematically evaluate this method against statistical baselines, state-of-the-art Transformers, and emerging foundation models using multi-year data from three distinct Danish districts, a Danish city, and a German city. The results show a significant advancement, reducing the Mean Absolute Error by 36% to 43% compared to the strongest baselines, achieving forecasting accuracy of up to 95% across annual test datasets. Qualitative and statistical analyses further confirm the accuracy and robustness by reliably tracking volatile demand peaks where others fail. This work contributes both a high-performance forecasting architecture and critical insights into optimal feature composition, offering a validated solution for modern energy applications.

Figures & tables

Figure 1: Hourly heat consumption data over the period from January 2016 to the end of December 2019 for DMA A. The outliers observed in the data identified through the Savitzky-Golay smoothing are marked using orange circles.

Panel of Figure 2 — Figure 2: Preprocessed hourly heat consumption data for DMA A. (a) Data from January 2016 to December 2019 after outlier removal. (b) A detailed view of the recorded heat consumption for two weeks in January 2017.

Figure 3: The distribution of Spearman correlation coefficients

\rho

between successive days of the week across different DMA .

Panel of Figure 4 — Figure 4: Short-term and long-term correlational analysis of heat demand data. (a) Spearman correlation $\rho$ between heat demand data and the lagged version of the heat demand data. Hourly lags equivalent to $1,2,...,28$ days are considered to evaluate short-term relationships. (b) Spearman correlation $\rho$ of weekly demand across 204 weeks comprised in the four-year heat demand dataset across different DMAs .

Feature Type	Feature	Spearman Correlation Coefficient ( $\rho$ )
		DMA A	DMA B	DMA C
Consumption	Lag of 24 hours ( $\textbf{c}_{24}$ )	0.973	0.975	0.970
	Lag of 168 hours ( $\textbf{c}_{168}$ )	0.923	0.920	0.918
Weather	Temperature ( $\textbf{t}_{\text{amb}}$ )	-0.907	-0.914	-0.911
	Minimum temperature ( $\textbf{t}_{\text{min}}$ )	-0.902	-0.910	-0.907
	Maximum temperature ( $\textbf{t}_{\text{max}}$ )	-0.921	-0.927	-0.924

Table 1: Available endogenous and exogenous features at an hourly resolution along with the respective Spearman correlation coefficient with demand.

Panel of Figure 5 — Figure 5: Spearman correlation coefficients between heat demand and key weather features across different DMA s. The heatmap(s) are structured in four rows, displaying correlations between: (1) actual heat demand and actual weather data; (2) their respective trend components; (3) their respective seasonal components; and (4) their respective residual components.

Figure 6: Seasonal decomposed demand data and maximum temperature sampled hourly for a specific DMA B for a period of one month showcasing the explicit relationship between respective components of demand and exogenous feature.

Figure 7: Wavelet CNN forecasting network with image-like multi-channel representation of scalograms as inputs for day ahead hourly demand forecasting.

Layer	Operator	Output Dimension	Kernel	Stride	Padding
Input	-	24 $\times$ 24 $\times$ $N_{\text{features}}$	-	-	-
Convolution 1	Conv2D + ReLU	24 $\times$ 24 $\times$ 32	3 $\times$ 3	1	1 (Same)
Convolution 2	Conv2D + ReLU	24 $\times$ 24 $\times$ 64	3 $\times$ 3	1	1 (Same)
Convolution 3	Conv2D + ReLU	24 $\times$ 24 $\times$ 128	3 $\times$ 3	1	1 (Same)
Flatten	Flatten	73728	-	-	-
Dense 1	Dense + LeakyReLU	1024	-	-	-

Table 2: Detailed architecture of the proposed CNN model with a total of

76,669,976

parameters. The input tensor dimensions correspond to (M

\times

N_{history}

\times

N_{features}

Feature Type	Original Vector	Decomposed Components	Decomposed Vector
Consumption	$\mathbf{c}_{24}\in\mathbb{R}^{24\times 1}$	Seasonal, Trend, Residual	$\mathbf{c}^{d}_{24}=\left([\mathbf{c}_{24}]\bigcup[\mathbf{c}^{trend}_{24},\mathbf{c}^{seas}_{24},\mathbf{c}^{resid}_{24}]\right)\in\mathbb{R}^{24\times 4}$
Consumption	$\mathbf{c}_{168}\in\mathbb{R}^{24\times 1}$	Seasonal, Trend, Residual	$\mathbf{c}^{d}_{168}=\left([\mathbf{c}_{168}]\bigcup[\mathbf{c}^{trend}_{168},\mathbf{c}^{seas}_{168},\mathbf{c}^{resid}_{168}]\right)\in\mathbb{R}^{24\times 4}$
Weather	$\mathbf{t}_{x}\in\mathbb{R}^{24\times 1}$	Trend, Residual	$\mathbf{t}^{d}_{x}=\left([\mathbf{t}_{x}]\bigcup[\mathbf{t}^{trend}_{x},\mathbf{t}^{resid}_{x}]\right)\in\mathbb{R}^{24\times 3}$

Table 3: Definition of raw and decomposed feature sets. The superscript

d

\mathbf{c}^{d}_{24}

\mathbf{c}^{d}_{168}

, and

\mathbf{t}^{d}_{x}

indicates the representations include decomposed components.

DMA	Features	MAE (kWh)	MAPE (%)	MSE ( $\times 10^{4}$ kWh 2 )
DMA A	$\textbf{c}_{24}$	$160.78\pm 114.56$	$8.1\pm 4.9$	$5.65\pm 9.09$
DMA A	$\textbf{c}_{24},\textbf{c}_{168}$	$165.98\pm 119.89$	$8.4\pm 5.2$	$5.95\pm 9.35$
DMA B	$\textbf{c}_{24}$	$300.87\pm 206.56$	$7.9\pm 4.6$	$18.32\pm 25.44$
DMA B	$\textbf{c}_{24},\textbf{c}_{168}$	$293.57\pm 203.57$	$7.7\pm 4.6$	$17.44\pm 24.22$
DMA C	$\textbf{c}_{24}$	$264.69\pm 172.27$	$7.7\pm 4.3$	$13.74\pm 18.52$
DMA C	$\textbf{c}_{24},\textbf{c}_{168}$	$260.04\pm 172.59$	$7.5\pm 4.2$	$13.43\pm 18.64$

Table 4: Comparison of model performance ( MAE , MAPE , and MSE ) for different endogenous features sets.

Panel of Figure 8 — Figure 8: Distribution of MAPE for models using only a 24-hour consumption lag ( $\textbf{c}_{24}$ ) versus both 24-hour and 168-hour lags ( $\textbf{c}_{24}$ , $\textbf{c}_{168}$ ). Performance is compared on days with sequentially similar patterns versus days with pattern disruptions across the three DMAs .

Model Features	MAE (kWh)	MAPE (%)	MSE (kWh ${}^{2}\times 10^{4}$ )
$\mathcal{M}_{C}$	$166.0\pm 119.9$	$8.40\pm 5.20$	$5.95\pm 9.35$
$\mathcal{M}_{C},\mathbf{t}_{\text{dew}}$	$149.1\pm 100.8$	$7.87\pm 4.83$	$4.73\pm 7.72$
$\mathcal{M}_{C},\mathbf{t}_{\text{min}}$	$130.4\pm 88.5$	$6.72\pm 3.85$	$3.65\pm 6.55$
$\mathcal{M}_{C},\mathbf{t}_{\text{feels}}$	$129.1\pm 94.2$	$6.58\pm 3.90$	$3.71\pm 6.85$
$\mathcal{M}_{C},\mathbf{t}_{\text{max}}$	$127.0\pm 87.7$	$6.41\pm 3.44$	$3.58\pm 6.84$
$\mathcal{M}_{C},\mathbf{t}_{\text{amb}}$	$122.7\pm 80.0$	$6.45\pm 3.50$	$3.21\pm 6.16$

Table 5: Performance metrics for various weather feature combinations for DMA A, sorted by MAE in descending order within each section. The base model,

\mathcal{M}_{C}

, includes consumption features. The best-performing model is highlighted in bold.

Model Features	MAE (kWh)	MAPE (%)	MSE (kWh ${}^{2}\times 10^{4}$ )
$\mathcal{M}_{C}$	$293.6\pm 203.6$	$7.70\pm 4.60$	$17.44\pm 24.22$
$\mathcal{M}_{C},\mathbf{t}_{\text{dew}}$	$250.4\pm 151.5$	$6.85\pm 4.15$	$12.30\pm 14.71$
$\mathcal{M}_{C},\mathbf{t}_{\text{min}}$	$221.6\pm 119.7$	$6.11\pm 3.35$	$9.13\pm 9.74$
$\mathcal{M}_{C},\mathbf{t}_{\text{feels}}$	$216.8\pm 127.1$	$5.83\pm 3.11$	$9.10\pm 11.18$
$\mathcal{M}_{C},\mathbf{t}_{\text{max}}$	$212.6\pm 121.0$	$5.64\pm 2.78$	$8.71\pm 9.78$
$\mathcal{M}_{C},\mathbf{t}_{\text{amb}}$	195.2 $\pm$ 104.3	5.21 $\pm$ 2.57	7.22 $\pm$ 7.43

Table 6: Performance metrics for various weather feature combinations for DMA B, sorted by MAE in descending order within each section. The base model,

\mathcal{M}_{C}

, includes consumption features. The best-performing model is highlighted in bold.

Model Features	MAE (kWh)	MAPE (%)	MSE (kWh ${}^{2}\times 10^{4}$ )
$\mathcal{M}_{C}$	$260.0\pm 172.6$	$7.50\pm 4.20$	$13.43\pm 18.64$
$\mathcal{M}_{C},\mathbf{t}_{\text{dew}}$	$241.0\pm 144.5$	$7.19\pm 4.31$	$11.15\pm 13.50$
$\mathcal{M}_{C},\mathbf{t}_{\text{feels}}$	$192.6\pm 116.7$	$5.63\pm 2.89$	$7.24\pm 9.59$
$\mathcal{M}_{C},\mathbf{t}_{\text{max}}$	$192.1\pm 103.5$	$5.74\pm 2.86$	$6.89\pm 7.84$
$\mathcal{M}_{C},\mathbf{t}_{\text{min}}$	$189.7\pm 106.1$	$5.64\pm 2.81$	$6.80\pm 8.35$
$\mathcal{M}_{C},\mathbf{t}_{\text{amb}}$	$176.7\pm 91.4$	$5.33\pm 2.62$	$5.80\pm 6.45$

Table 7: Performance metrics for various weather feature combinations for DMA C, sorted by MAE in descending order within each section. The base model,

\mathcal{M}_{C}

, includes consumption features. The best-performing model is highlighted in bold.

DMA	Features	MSE (kWh ${}^{2}\times 10^{4}$ )		MAPE (%)		MAE (kWh)
DMA	Features	Original	Decomposed	Original	Decomposed	Original	Decomposed
DMA A	$\mathcal{M}_{C},\mathbf{t}_{\text{max}}$	3.58	2.64	6.41	5.47	127.0	106.1
	$\mathcal{M}_{C},\mathbf{t}_{\text{feels}}$	3.71	2.68	6.58	5.53	129.1	105.7
	$\mathcal{M}_{C},\mathbf{t}_{\text{amb}}$	3.21	2.39	6.45	5.50	122.7	102.8
	$\mathcal{M}_{C},\mathbf{t}_{\text{min}}$	3.65	2.64	6.72	5.67	130.4	107.1
	$\mathcal{M}_{C},\mathbf{t}_{\text{max}},\mathbf{t}_{\text{feels}}$	3.33	2.69	6.22	5.68	123.4	108.6

Table 8: Unified comparison of model performance across all DMAs for models with raw features versus those with decomposed features.

DMA	Features	MSE (kWh ${}^{2}\times 10^{4}$ )	MAPE (%)	MAE (kWh)	Wilcoxon Signed-Rank Test p-value
DMA A	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}}$	2.45	5.37	101.7	$>0.05$
DMA A	With Time Features ( $+T_{\text{cyc}}$ )	2.44	5.50	103.0
DMA B	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{max}},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}}$	5.35	4.46	165.5	$<0.05$
DMA B	With Time Features ( $+T_{\text{cyc}}$ )	5.93	4.93	176.3
DMA C	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{max}},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}}$	4.43	4.65	152.6	0.035
DMA C	With Time Features ( $+T_{\text{cyc}}$ )	5.06	4.90	161.0

Table 9: Performance comparison of models with and without cyclical time features (

+T_{\text{cyc}}

). The temporal features are added to the best performing decomposed models: [

\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}}

] for DMA A , and [

\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{max}},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}}

] for DMA B and DMA C .

DMA	Holiday Handling Method	MSE ( $\times 10^{4}$ kWh 2 )	MAPE (%)	MAE (kWh)
DMA A	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}}$	$2.45\pm 5.47$	$5.4\pm 3.3$	$101.73\pm 71.75$
	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}},\mathbf{h}_{categorical}$	$2.46\pm 5.58$	$5.5\pm 3.4$	$103.42\pm 71.32$
	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}},\mathbf{h}_{lagged}$	$2.51\pm 5.54$	$5.6\pm 3.3$	$104.84\pm 71.03$
	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{t}^{d}_{\text{min}},\mathbf{h}_{lagged},\mathbf{h}_{categorical}$	$\mathbf{2.36\pm 5.42}$	$\mathbf{5.3\pm 3.3}$	$\mathbf{99.76\pm 72.71}$
DMA B	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{max}},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}}$	$5.35\pm 5.99$	$4.5\pm 2.3$	$165.48\pm 88.42$
	$\mathcal{M}^{d}_{C},\mathbf{t}^{d}_{\text{max}},\mathbf{t}^{d}_{\text{feels}},\mathbf{t}^{d}_{\text{amb}},\mathbf{h}_{categorical}$	$5.63\pm 6.22$	$4.8\pm 3.0$	$171.97\pm 90.57$

Table 10: Performance comparison of different holiday handling strategies. The model with their best performance features are compared against three approaches: adding holiday as a categorical feature

\mathbf{h}_{categorical}

, replacing the feature

C_{168}

with the consumption values of the previous occurrence of the same holiday

\mathbf{h}_{lagged}

, and combining both strategies

\mathbf{h}_{categorical}

and

\mathbf{h}_{lagged}

Panel of Figure 9 — Figure 9: Model Error ( MAE ) on public holidays in Denmark comparing different embeddings of holiday features across three DMAs (a) DMA A, (b) DMA B, and (c) DMA C.

Panel of Figure 10 — Figure 10: Distribution of MAPE across the three DMAs comparing different embeddings of holiday features for holiday and non-holiday samples with comparison to the baseline without holiday features. The box plots in (a), (b), and (c) show the model error for DMA A, DMA B, and DMA C, respectively.

Architecture	DMA A			DMA B			DMA C
Architecture	MAE	MAPE	MSE	MAE	MAPE	MSE	MAE	MAPE	MSE
Preformer	$320.68$	$21.37$	$1.69$	$627.20$	$21.12$	$6.37$	$552.04$	$19.34$	$4.99$
Autoformer	$241.86$	$11.52$	$1.03$	$385.94$	$12.51$	$2.62$	$387.36$	$11.97$	$2.61$
Informer	$208.51$	$9.42$	$0.79$	$306.92$	$9.30$	$1.75$	$312.38$	$9.23$	$1.77$
TTM Fine-tuned	$191.47$	$10.08$	$0.73$	$320.25$	$8.28$	$1.98$	$301.66$	$8.49$	$1.71$
LSTM	$187.62$	$9.56$	$0.71$	$327.49$	$8.70$	$2.06$	$295.44$	$8.32$	$1.67$

Table 11: Quantitative results comparing existing statistical, state-of-the-art methods, and foundation models for hourly heat demand forecasting with our proposed approach for a forecasting horizon of 24 hours. MAE is in kWh , MAPE in %, and MSE in

10^{5}\text{kWh}^{2}

Panel of Figure 11 — Figure 11: Quantitative comparison of MAE of different models for the respective DMAs of (a) DMA A, (b) DMA B, and (c) DMA C. The proposed approach (far right) demonstrates lower median error and reduced variance compared to DL and statistical baselines.

Panel of Figure 12 — Figure 12: Qualitative forecast comparison for the week with the highest error across all three districts: (a) DMA A (2019-04-08 to 2019-04-14), (b) DMA B (2019-01-14 to 2019-01-20), and (c) DMA C (2019-01-14 to 2019-01-20). These plots highlight model performance during highly volatile demand periods, showcasing the robustness of our approach compared to baselines.

Panel of Figure 13 — Figure 13: Qualitative forecast comparison for the week with the lowest error across all three districts: (a) DMA A (2019-08-05 to 2019-08-11), (b) DMA B (2019-08-05 to 2019-08-11), and (c) DMA C (2019-07-15 to 2019-07-21). These plots show performance during stable, predictable demand, where all models perform reasonably well.

Panel of Figure 14 — Figure 14: Qualitative forecast comparison for the top five days of worst forecasts across all three districts: (a) DMA A, (b) DMA B, and (c) DMA C.

Panel of Figure 15 — Figure 15: Qualitative forecast comparison for the top five days of best forecasts across all three districts: (a) DMA A, (b) DMA B, and (c) DMA C.

Panel of Figure 16 — Figure 16: Distribution of Mean Absolute Error (MAE) across different years for the three DMAs (top row) and the two city-level datasets (bottom row).

Panel of Figure 17 — Figure 17: Distribution of Mean Absolute Error (MAE) across different years for the three DMAs (top row) and the two city-level datasets (bottom row).

Abbreviations

AIC	Akaike Information Criterion	MAE	Mean Absolute Error
CNN	Convolutional Neural Network	MAPE	Mean Absolute Percentage Error
CWT	Continuous Wavelet Transform	ML	Machine Learning
DHS	District Heating Systems	MLP	Multi-Layer Perceptron
DL	Deep Learning	MLR	Multiple Linear Regression

Table 29

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 18: Quantitative comparison on the effect of employing dropout with varying probabilities and the effect of pooling layer on the forecasting performance.

Figure 19: Quantitative evaluation comparing the effect of candidate mother wavelet for CWT on the forecasting performance in terms of MAE for DMA A

Hyperparameter	Search Space / Grid	Selected Value
Training Dynamics
Learning Rate ( $\eta$ )	$\{0.01,0.001,0.0001\}$	$0.001$
Batch Size	$\{16,32,64,256\}$	$32$
Feature Transformation
	mexh, morl	morl (DMA A, C) gaus8 (DMA B)
Mother Wavelet Candidate	gaus1-gaus8, cgau1-cgau8

Appendix

Table 12: Hyperparameter search space and selected values for the proposed Wavelet-CNN framework.

Panel of Figure 20 — Figure 20: Illustration of training and validation loss curves for the proposed Wavelet-CNN models trained for a maximum of 1000 epochs with a patience 50 epochs. The box plots in (a), (b), and (c) show the loss curves for DMA A, DMA B, and DMA C, respectively.

Dataset	Training Time (min)	Inference Latency (ms/sample)
DMA A	$2.76\pm 0.26$	$0.23\pm 0.14$
DMA B	$3.10\pm 0.46$	$0.24\pm 0.17$
DMA C	$2.48\pm 0.11$	$0.22\pm 0.14$
Average	$\mathbf{2.78\pm 0.24}$	$\mathbf{0.23\pm 0.15}$

Appendix

Table 13: Computational efficiency metrics per DMA . Values represent the Mean

\pm

Standard Deviation across 5 iterations. Inference latency is reported in milliseconds per sample.

Hyperparameter	Search Space	Selected Value
N Estimators	{200, 400, 600, 800, 1000, 1500, 2000}	200
Learning Rate	{0.1, 0.01, 0.001, 0.0001}	0.1
Maximum Depth	{2, 4, 6, 8, 10, 12, 24}	4
Subsample	[0.6, 0.7, 0.8, 0.9, 1.0]	0.8

Appendix

Table 14: Hyperparameter tuning for the XGBoost model.

Hyperparameter	Search Space	Selected Value
LSTM Layers	{1, 2, 4}	4
LSTM Hidden Units	{16, 32, 64, 128}	32
Learning Rate	{1e-4, 5e-4, 1e-3}	1e-3

Appendix

Table 15: Hyperparameter tuning for the LSTM model.

Hyperparameter	Search Space	Informer	Autoformer	PatchTST	DLinear	TimesNet	TimeMixer
General Training Parameters
Learning Rate	{0.01, 0.001, 0.0001}	0.0001	0.0001	0.0001	0.001	0.0001	0.001
Dropout	$[0.05,0.3]$	0.1	0.1	0.1	0.1	0.1	0.1
Common Architectural Parameters
$d_{model}$	{32, 64, 256, 512, 1024}	512	1024	512	–	1024	32
$n_{heads}$	{4, 6, 8, 10}	6	8	8	–	8	–

Appendix

Table 16: Hyperparameter search space and final configurations for Deep Learning baselines. All models were tuned using Optuna. The search space reflects the grid swept during the 50-trial optimisation process.

Date (2019)	Day of the Week	Danish Name	English Translation
2019-01-01	Tuesday	Nytårsdag	New Year’s Day
2019-04-18	Thursday	Skærtorsdag	Maundy Thursday
2019-04-19	Friday	Langfredag	Good Friday
2019-04-21	Sunday	Påskedag	Easter Sunday
2019-04-22	Monday	Anden påskedag	Easter Monday
2019-05-17	Friday	Store bededag	Great Prayer Day

Appendix

Table 17: Translation and Day of the Week for Danish Holidays (2019).

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District heating energy hubs require reliable heat load forecasts for efficient operational scheduling. Forecasting models trained on historical data may require retraining as networks evolve. Zero-shot time-series foundation models and in-context forecasting therefore offer a promising alternative: they can adapt at inference time from recent observations rather than by repeated retraining. This study systematically evaluates TabPFN-TS and Chronos-2 for probabilistic heat load forecasting in two German district heating networks and compares them with trained baselines. We assess whether TabPFN-TS, whose underlying model is pretrained entirely on synthetic tabular rather than time-series data, can capture complex district heating dynamics. We analyze covariate choice, context length, temporal resolution, and forecast horizon on selected operating weeks, evaluate the selected configuration over the full year, and assess cross-network transfer. The principal benchmark assumes perfect weather forecasts; a separate sensitivity analysis uses retrospective weather predictions. Hourly 24-hour forecasting with a 12-week rolling context and ambient temperature provides a parsimonious configuration; longer context windows do not improve accuracy. Both TSFMs outperform all trained baselines in deterministic accuracy in the full-year benchmarks. Chronos-2 achieves the best deterministic scores, with TabPFN-TS remaining close: their CVRMSE values on the main data set are 12.48% and 13.07%, respectively. Chronos-2 also achieves lower continuous ranked probability scores in both networks, with TabPFN-TS remaining close. a TSFM-based Multi-Resolution Residual-Correction Forecaster combines an hourly base forecast with short-term high-resolution corrections. Relative to direct high-resolution forecasting, it generally reduces errors in total heat demand over 12-hour periods and recorded prediction times.

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