The studied problem concerns the optimal regulation with a fixed horizon of two vertical ovens having respectively three or twelve heating areas. The model of the thermal process is described thanks to a linear state equation with a quadratic criterion to minimize. Furthermore, the terminal state is fixed and the state is subjected to some constraints. We propose and analyze the relaxation method coupled with the shooting method to solve this problem. The convergence of the numerical procedure is presented. Numerical experiments are done and validate our approach.