A method is proposed for the computation of the transient heating of a conductor in which eddy currents flow, induced by time-harmonic source currents. The electrical field is assumed as unknown on a mesh of edge elements and is computed by a time-harmonic analysis. The heating power density inside the conductor is computed and a transient thermal analysis is started on the same mesh of nodal elements. This analysis is continued until the temperature-dependent electrical conductivity changes enough to require another time-harmonic eddy-current analysis. The combined procedure is iterated.