Design and experimental validation of model predictive control (MPC) of a hybrid dynamical laboratory process with wireless sensors is presented. The laboratory process consists 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. The process, which is motivated by heating processes in the plastic and printing industry, presents interesting hybrid dynamics. 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 setpoints and lamp on/off commands over a wireless link, exploiting the sensor 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. The physical modelling of the process and the hybrid MPC algorithm are presented in detail, together with the hardware and software architectures. The experimental results show that the presented theoretical framework is well suited for control of the new laboratory process, and that the process can be used as a prototype system for evaluating hybrid and networked control strategies.