The model predictive control (MPC) for optimal temperature control in building is designed in order to reduce the energy consumption while respecting occupant comfort, assuming that the comfort in this work is defined by a reference temperature. MPC is developed and applied first to a simplified case where no disturbance is considered then a measured disturbance representing predictive knowledge of weather conditions is integrated. As the application of MPC requires a dynamical model, thus the single zone building considered is modeled.