This paper presents the design and the experimental validation of model predictive control (MPC) of a hybrid dynamical process based on measurements collected by a wireless sensor network. The proposed setup is the prototype of an industrial application in which a remote station controls the process via wireless network links. The experimental platform is a laboratory process consisting of four infrared lamps, controlled in pairs by two on/off switches, and of a transport belt, where moving parts equipped with wireless sensors are heated by the lamps. By approximating the stationary heat spatial distribution as a piecewise affine function of the position along the belt, the resulting plant model is a hybrid dynamical system. The control architecture is based on the reference governor approach: the process is actuated by a local controller, while a hybrid MPC algorithm running on a remote base station sends optimal belt velocity set-points and lamp on/off commands over a network link exploiting the information received through the wireless network. A discrete-time hybrid model of the process is used for the hybrid MPC algorithm and for the state estimator.