Linear DC motors (LDPT) with a limited armature stroke are used in mechanisms that reciprocate the working body or stabilize its position in tracking systems. The use of LDPT instead of rotary motion motors with a converter in the form of a crank mechanism, a screw pair or other similar mechanical systems leads to a significant simplification of the kinematic scheme, increased efficiency and, as a rule, increased accuracy of the complex and its reliability. There are a number of problems in the creation of LDPT, which are not fully reflected in the scientific and technical literature. In particular, with parametric optimization of the engine according to weight, size and energy criteria, one of the main limiters is overheating of the winding, and in magnetoelectric machines, also overheating of permanent magnets, which are very sensitive to the magnitude of the operating temperature and thermal shocks. The article presents an analytical method for calculating the thermal state of an engine in steady state, based on the method of thermal substitution schemes. The technique is designed for use in a parametric optimization program. To clarify the values of the a priori coefficients in the analytical expressions of the proposed algorithm, the authors modeled the LDPT using the numerical finite element method. Based on the simulation results, a picture of the temperature field of the machine was obtained and the critical heating areas were determined. Verification of the theoretical provisions was carried out during experimental studies of the prototype engine. The tests showed good convergence of the calculated and experimental parameters.