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Modern Multiprocessor Systems-on-Chip (MP-SoC) offer high computing performance at the expense of huge power densities unevenly distributed on the chip. This generates hot spots that may cause performance and reliability degradations as well as power consumption increases. In recent years several thermal control strategies have been developed to avoid the occurrences of these hot spots. In particular, schemes based on Model Predictive Control (MPC) theory represent the actual state-of-the-art due to their capability to explicitly deal with constraints. In this paper we discuss some important properties for the design of predictive controllers with constraints for the class of thermal system. Starting from the general partial differential equation representing the heat diffusion in a solid, the feasibility and a useful property for the reduction of the number of constraints are proven. Moreover, exploiting theoretical results, a two layers control architecture is presented, which is capable of ensuring feasibility in every circumstance. Simulative results show the benefits of this approach.