The real-time predictive dynamic operation of building thermal systems is explored in this paper. A systematic methodology is described for predictive supervisory operation. The focus of this study is on the development of an operation supervisor that can determine optimal operation strategies for building thermal processes, and its application to a floor heating system in a passive solar room with thermal mass. An optimal model associated with a number of practical operation constraints is formulated, and an approach that combines dynamic programming and on-line simulation is developed, to efficiently solve the problem in real-time. Simulations for the minimisation of energy consumption and operating cost, with different operation schedules under various weather conditions. are performed. Results show that the techniques are computationally efficient and that the predictive supervisory operation of floor heating systems may lead to significant savings in energy consumption and operating cost. (C) 2001 Elsevier Science B.V. All rights reserved.