The paper describes a predictive and adaptive heating controller, using artificial neural networks to allow the adaptation of the control model to the real conditions (climate, building characteristics, user's behaviour). The controller algorithm has been developed and tested as a collaborative project between the CSEM (Centre Suisse d'Electronique et de Microtechnique, Neuchâtel, Switzerland, project leader), and the LESO-PB (Solar Energy and Building Physics Laboratory, EPFL, Lausanne, Switzerland). A significant support has been provided by leading Swiss industries in control systems. The project itself has been funded by the Swiss Federal Office of Energy (SFOE). The project has allowed the development of an original algorithm, especially suited for water heating systems, and its testing both by simulation and by experimentation on an inhabited building. The experimentation has been done using a PC software implementation. A second phase of the project, currently going on, aims at building a commercial system based on the NEUROBAT algorithm.