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Prediction of heat demand using artificial neural networks has attracted enormous research attention. Weather conditions, such as direct solar irradiance and wind speed, have been identified as key parameters affecting heat demand. This paper employs an Elman neural network to investigate the impacts of direct solar irradiance and wind speed on the heat demand from the perspective of the entire district heating network. Results of the overall mean absolute percentage error (MAPE) show that direct solar irradiance and wind speed have quite similar impacts. However, the involvement of direct solar irradiance can clearly reduce the maximum absolute deviation when only involving direct solar irradiance and wind speed, respectively. In addition, the simultaneous involvement of both wind speed and direct solar irradiance does not show an obvious improvement of MAPE. Moreover, the prediction accuracy can also be affected by other factors like data discontinuity and outliers.