General description of the research topic. A technique and an algorithm for calculating the thermal field of electromagnets operating in complex forced systems proposed by authors are considered. The widespread use of such devices in electromechanical switching devices allows not only to increase their speed but also significantly reduce the size, mass and energy losses, which indicates the relevance of this topic. The mathematical model of heating the windings of forced electromagnets proposed by the authors is a system of 1D differential equations of stationary heat transfer in a cylindrical coordinate system, supplemented by equations of electrical and magnetic circuits. This model allows to take into account the ripple of the currents in the windings and the losses in the magnetic core due to these ripples, contains certain signs of scientific novelty and represents the goal of the paper. The algorithm developed by the authors for calculating the thermal field of electromagnets operating in forced control systems is a complex iterative cycle. Its implementation is greatly simplified by using the Maple computing environment which allows to realize complicated and cumbersome mathematical transformations, automates the process of computations, and obtain results of numerical simulation in a convenient tabular and/or graphic form, which indicates the practical significance of this works. The results of comparison of computation results with experimental data presented in the paper indicate the adequacy of the model and algorithm proposed. References 17, tables 1, figures 7.