Stochastic models for the analysis of the energy and thermal comfort performances of passive solar devices have benn increasingly studied for over a decade. A new approach to thermal building modelling, based on Markov chains, is proposed here to combine both the accuracy of traditional dynamic simulation with the practical advantages of simplified methods. A main difficulty of the Markovian approach is the discretization of the system variables. Efficient procedures have been performed to carry out this discretization and several numerical experiments have been performed to analyze the possibilities and limitations of the Markovian model. Despite its restrictive assumptions, it will be shown that accurate results are indeed obtained by this method. However, due to discretization, computer memory requirements are more than inversely proportional to accuracy.