In this work, we deal with a mathematical model of heat induction processes. We first build a model derived from Maxwell and heat equations and, using certain simplifying assumptions, we obtain a system of coupled partial differential equations describing the evolution of thermal and magnetic fields. We show that this evolutive problem has a solution in a weak sense. The study of the problem is carried out using numerical analysis techniques. A numerical scheme is build to be implemented on a computer in order to obtain numerical results. Finally, we present theoretical results for a steady-state problem and prove existence of a solution under assumptions weaker than in the evolutive case.