Artificial neural networks (ANNs) can be used for accurate heat load forecasting in district heating systems (DHSs). This paper presents an application of a shallow ANN with two hidden layers in the case of a local DHS. The developed model was used to write a simple application in Python 3.10 that can be used in the operation of a district heating plant to carry out a preliminary analysis of heat demand, taking into account the ambient temperature on a given day. The model was trained using the real data from the period 2019–2022. The training was sufficient for the number of 150 epochs. The prediction effectiveness indicator was proposed. In the considered case, the effectiveness of the trained network was 85% and was better in comparison to five different regression models. The developed tool was based on an open-source programming environment and proved its ability to predict heating load.