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This paper proposes to apply optimal multiphysic models to the design of highly constrained electrical machines, such as interior permanent-magnet (IPM) machine intended for an automotive integrated starter generators. One of the main problems in the use of such optimal approaches remains the accuracy of the models used by the optimizer. In a recent study, we proposed a design model linked to three strong hypotheses: 1) Iron losses are calculated according to the flux density fundamental (sinusoidal approach); 2) flux densities are estimated with a saturated but decoupled d,q reluctant circuit model neglecting the cross saturation effect; and 3) thermal states are indirectly treated with a current density limit. This paper improves these models by using first the finite element method for the determination of flux and iron losses in the machine and then an equivalent thermal steady-state lumped-parameter network. These models are included in the optimization loop and so are evaluated at each iteration. The optimization method uses standard sequential quadratic programming algorithm and Sequential Simplex algorithm. A comparison between the design of an IPM machine with the previous model and the new one will be performed.