This paper presents a complete modeling of a multi-phase induction system for metal disc heating. It proposes a global solution including electrical and thermal modeling of the whole system in PSim software, with a reduced simulation time. It is based on simplified equivalent models but takes into account data extracted from finite element software for the transfer between the coil currents and the piece to be heated. The knowledge of the current density distribution extracted from the finite element software Flux2D and the impedance matrix that describes the electrical behaviour of the three coils supplied by current source inverters made it possible. A specific optimisation procedure allows us to calculate the optimal supply currents in the inverters in order to obtain a uniform heating of the work piece. As a result, the experimental thermal distributions are in good agreement with simulated ones.