The reduction of the energy consumption in buildings has become a priority in every developed country. Automatic control is one of the latest techniques introduced to this purpose. This paper describes the design of a new controller which controls the internal temperature of an individual dwelling by adjusting of the heating power. First, considering the intermittency the occupation, an optimal temperature trajectory in term of control cost has been computed. Second, introducing an augmented state representation, a state feedback law has been calculated. Third, since this law required an inaccessible state, a Kalman estimator has been introduced to estimate this state. Introducing a deconvolution problematic in its design, a “virtual feed forward” based on estimation has been introduced to balance the external disturbances. Fourth, in order to take into account the control saturation of the heating system, an anti-windup compensator has been introduced to the controller. Finally, the controller has been tested in simulation on an experimental building and the interest of the virtual feed forward has been illustrated.