Optimizing the operation of heating systems in buildings has become of high interest. The control objective of such systems is to minimize the heating energy bills while maintaining a certain indoor thermal comfort. Dealing with electric convectors, the heating price is proportional to the amount of heat delivered. Hence, using a linear model of the process in an MPC environment, the optimization problem can be stated in an LP form. In this paper we treat the case of multi-zone building temperature regulation, where the available electrical power is lower than the sum of the maximum powers of local heaters. This acts as a coupling constraint in our optimization problem. A distributed MPC (DMPC) algorithm based on Dantzig-Wolfe decomposition is proposed, considering also the thermal coupling between adjacent zones. Numerical results are presented in order to illustrate the effectiveness of the proposed control strategy.