The paper presents a mathematical model for the numerical simulation of a substation for the supply of hot water which operates without auxiliary energy. The introduced original mathematical model has been verified experimentally, enabling a direct comparison with real conditions. While the approach to the mathematical modelling is traditional, the main innovation is the selection and derivation of suitable mathematical models, which are able to deliver the results which are as close as possible to real conditions, thus enabling an excellent accordance of both models, i.e. the mathematical simulation and the test line results. The simulated system is modular to allow analysis of the influence of each parameter. The non-linear model was applied for the heat exchanger, while the temperature sensor has been modeled as the second order system to account for its heat conducting protective pocket. When modelling the valve, its dynamic characteristics have been considered, being an additional advantage over existing mathematical models. The reason for research is to optimize water heaters, a common solution for hot water services in Nordic countries. (C) 2005 Elsevier B.V. All rights reserved.