The paper is devoted to the issues of thermoelasticity of an elliptical cylinder under boundary conditions of the first kind. At the same time, a heat source of the same magnitude acts inside the cylinder. It deals with the distribution of the temperature field of a rod of elliptical cross-section under specified boundary conditions. The main method is the substitution method. The resulting expression of the temperature field of the cylinder has an analytical form containing a hyperbolic sine. This allows us to judge the nature of the temperature distribution over the cross-section of the rod. The thermoelasticity problem itself is solved by determining the stress function. The level of thermal stresses that occur was also investigated based on the differentiation method. The result obtained can be used in engineering calculations of heat exchangers.