This paper presents an original approach which makes use of a realistic thermal model for adaptive predictive control and supervision of a semibatch jacketed reactor. The first part is devoted to the development of an adaptive controller based on a realistic model established by thermal balances on the reactor and its jacket. As a first interest, an on-line deterministic estimator of the heat generated during the reaction is developed. In a second part a realistic model is used for model supported supervision to prevent temperature overshoot, especially in the case of industrial reactors, the temperature control being ensured by the adaptive controller.