This article treats the problem of modeling and controlling a multi-zone office building to ensure its hygrothermal comfort through optimal and cost-effective management. An analysis of the hygrothermal behavior is carried out, which leads to a set of descriptor state-space models. Based on this modeling, an iterative algorithm is proposed to solve the optimization problem associated to the model predictive control (MPC) design. By means of an original cost function based on peak/no peak energy consumption, significant energy savings can be envisaged in practice.