This paper focuses on the use of a technique of Space Mapping (SM) for the optimization of a Permanent Magnet Machine (PMM) used as an Integrated Starter Generator (ISG). To demonstrate the benefits of such a design approach, it has been applied in the context of a realistic and very constrained application, particularly from the thermal point of view. Thus, this actuator is considered to function in start mode during which the rotation speed is low and thermal sources (mainly copper losses) are very high for a short time. Indeed, it is necessary to consider temperature increases versus time, as if several consecutive starts were imposed to the machine (car). To realistically simulate the operation of the motor, significant efforts were made to improve the quality of multi-physical modelings, especially regarding thermal aspects. Finite Element Analyses (FEA) are used for the evaluation of the electromagnetic behavior. Temperature distributions are computed by the use of equivalent lumped parameter networks, while mechanical considerations are taken, through analytical relations, to ensure the mechanical holding of rotating parts. Finally, physical couplings (between models) constitute important considerations. They are essentially related to mechanical, copper and iron losses. SM techniques operate on two (multi-physical) modelings of the same machine. Hence, using this optimization approach requires the definition of two sets of magnetic-electric-mechanical-thermal descriptions of the PMM to be dimensioned. This paper presents the choices made for their building, and the results obtained.