The problem of analysis of non-stationary heat generation due to the flow of electric current in devices for magnetic-pulse processing of materials is considered. An analysis of the available information sources led to the conclusion that a large number of studies in this area are devoted to the study of heat transfer processes during technological operations of induction heating. In other technological operations of magnetic-pulse processing of materials, heat release is also significant. In this case, a non-stationary inhomogeneous temperature field can lead to significant temperature deformations. This, in turn, can cause a loss in the performance of the device due to destruction or irreversible deformation. Adequate modeling of non-stationary temperature propagation in this case is an obligatory step in carrying out computational analysis in the process of designing technological devices. A general strategy is proposed for determining the propagation of a non-stationary temperature field in the presence of a non-stationary non-uniform electromagnetic field. The proposed strategy presupposes a general solution of the problems of the propagation of the electromagnetic field and the temperature field within the framework of a unified design scheme. The use of the finite element method is proposed as a numerical method. The finite element method, when used in such problems, allows one to draw up iterative procedures that can be used to take into account the nonlinear effects associated with the influence of temperature on the electro-physical properties of materials. The problem of sequential determination of a non-stationary, non-uniform electromagnetic field and a non-stationary temperature field in composite matrices intended for electromagnetic pressing of powders of super-strong refractory materials is considered. The distribution of some quantitative characteristics of the electromagnetic field, as well as the dependence of temperature on time are presented.