Abstract This paper presents the comparison of three data driven models for short-term thermal behaviour prediction in a real building, part of a living smart district connected to a thermal network. The case study building is representative of most of the buildings of the tertiary sector (e.g. offices and schools) built in Italy in the 60s–70s of the 20th century. The considered building models are: three lumped element grey-box models of first, second and third order, an AutoRegressive model with eXogenous inputs (ARX) and a Nonlinear AutoRegressive network with eXogenous inputs (NARX). The models identification is performed by means of real measured data. Nevertheless the quantity and quality of the available input data, all the data driven models show good accuracy in predicting short-term behaviour of the real building both in winter and summer. Among the grey-box models, the third order one shows the best performance with a Root-Mean-Square Error (RMSE) in winter less than 0.5 °C for a prediction horizon of 1 h and a RMSE less than 1 °C for a prediction horizon of 3 h. The ARX model shows a maximum RMSE less than 0.5 °C for a prediction horizon of 1 h and a RMSE less than 0.8 °C for a prediction horizon of 3 h. The NARX network shows a maximum RMSE less than 0.5 °C for a prediction horizon of 1 h and a RMSE less than 0.9 °C for a prediction horizon of 3 h. In summer the RMSE is always lower than 0.4 °C for all the models with a 3-h prediction horizon. Other than typical control applications, the paper demonstrates that all the data driven models investigated can also be proposed as a powerful tool to detect some typologies of occupant bad behaviours and to predict the short-term flexibility of the building for demand response (DR) applications since they allow a good estimation of the building “thermal flywheel”.