This paper presents a new numerical approach to model the heat transmission over long pipes, such as those encountered in district heating networks. The model is suitable for fast and accurate simulation of complex network dynamics. For fast calculation, the model is based on the method of characteristics. For high accuracy, the model splits the water thermal capacity between the turbulent core and the boundary layer. Compared with the finite-volume method and the node method, the proposed model shows accurate results at a lower computational expense and without introducing artificial smoothing of temperature waves. The model is validated by monitoring data of pronounced temperature transients in real pipes at low and high Reynolds numbers. The results confirm the need to properly model the thermal capacity of water, because at a low Reynolds number, the boundary-layer thickness is considerable, and the temperature difference between the water core and the pipe wall is not negligible. •Heat-transmission model based on the method of characteristics.•Inclusion of the thermal capacity effect related to the turbulent boundary layer.•Calculation 103 times faster than the finite-volume method at the same level of accuracy.•Very good agreement with experimental data.