This paper considers a computational algorithm for the thermoelastic state of a rod clamped at two ends in the presence of a heat flow on its side surface, varying along the coordinates by a quadratic law. The corresponding computational algorithms developed by the author make it possible to solve a class of engineering problems in determining the elongation of rods of limited length. The corresponding computational algorithms developed by the author make it possible to solve a class of engineering problems in determining the elongation of rods of limited length. Therefore, undoubtedly, the results of this work can be widely used in enterprises where calculations are carried out to determine the distribution laws of temperature fields and elongations of structural rod elements operating in a thermal field and in the presence of mechanical forces. The study of compression of a rod of limited length clamped at two ends under the influence of a temperature field and heat flow that varies along the length is of relevant interest for engineering and technological processes related to the strength of partially thermally insulated structural elements operating under coordinate-variable steady-state thermal fields. The relevance of these problems is also motivated by the fact that many structural elements operate under the simultaneous influence of axial force, coordinate-variable heat flow, heat exchange and thermal insulation. With the simultaneous consideration of the above factors, the analytical solution of steady-state thermoelastic compression and tension of rods becomes very complex. In this regard, there naturally arises the need to develop appropriate mathematical models of universal computational algorithms that make it possible to study the thermoelastic state of partially thermally insulated one-dimensional structural elements in the presence of heat exchange with the environment, a variable coordinate of the heat flow field and axial forces.