This paper presents an exhaustive study about the propulsion force and the thermal performance of the double-sided flat Linear Switched Reluctance Motor (LSRM) according to the number of phases (m) and the pole stroke (PS). The analysis is performed by means of the Finite Element Method (FEM) for electromagnetic computations and a lumped parameter for thermal model (LPT) both linked to an optimization algorithm based on the Response Surface Methodology (RSM) in order to reduce the computing time. The results show the optimal design of LSRM from the point of view of the thermo-mechanical performance for a given insulation class and a duty cycle operating conditions.