The remainder of this paper is organized as follows. In Section 2, the dynamics of the heated hold-up tank is presented with more details as well as the framework of PDMP’s. In Section 3 the formulation of the optimal stopping problem for PDMP’s and its theoretical solution are briefly recalled and the four main steps of the algorithm are detailed. In Section 4 the numerical results obtained on the example of the tank are presented and discussed. Finally, in Section 5 a conclusion and perspectives are presented.