The handling of mission-critical devices, e.g. electro-mechanical actuators, requires an exact calculation of the electromagnetic field. For this kind of task thermal influences on the electrical behaviour cannot be neglected.  Furthermore stationary solutions will not longer be  sufficient for the coupled problem.  We combined the Maxwell equations excluding displacement currents together with the instationary heat transfer equations into the finite difference program code PROFI. The stationary solutions of this coupled problem provide initial conditions for the instationary problem only.  Because in the stationary case the solutions of these coupled electro-thermal systems converge often slowly, we implemented a faster algorithm, based on the inclusion of linearized coupling terms between both field equations. A significant speedup has been achieved.  For the analysis of instationary processes, both field problems are solved simultaneously in the time domain. To ensure stability and physical reliability, the necessary criteria are fulfilled by means of a variable time-step algorithm in conjunction with automatically adapted coefficients for the implicit solution scheme.  The accuracy of the method will be illustrated by applying to a switched relay coil. For the stationary case  as well as the instationary behavior has been achieved  an excellent correspondence between the numerical and experimental data. Also the influences of different thermal models for regions with mixed materials, like coils built of insulated wires are discussed.