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A method for the induction heating problem solution in three dimensions is presented. This method couples the transient heat conduction equation, associated to convective and radiative boundary conditions with the electromagnetic system modeled by the A*- Psi - phi method. The nonlinearities associated to the variation of parameters with the temperature as well as the modeling of the Curie point are included. Particular attention is given to the time stepping scheme which allows a time-step variation based on the estimation of the error due to time discretization and to the incomplete solution of the problem's nonlinearity. This generates a method which avoids the need of iterative calculations in each time step of the nonlinear coupled problem.