The rapid heating of a circular conducting plate by a magnetic field decaying exponentially with time and its transition to a final steady-state is studied for the cases of both isolated and non-isolated plates. Analytic expressions are derived for the thermal field, the heat flux and the relaxation times. Both the ’‘thin” and the “thick” aspects of the problem are investigated. Emphasis is placed upon some characteristic parameters arising from the analytical solution. Attention is paid to the time constants, related to the combined (conduction and convection) thermal process. In fact, the ratio of these time constants determines the transition process up to the final steady-state of each region of the plate.