A non-stationary boundary value problem of thermodynamics is considered, useful for analyzing the thermal stress state of various rod structures under various force effects under thermal heating conditions. The Cauchy problem is solved, the solution of which allows one to determine the state of the rod at any time, provided that its initial state and the current sources of power and heat are known. Using the model of uncoupled thermoelasticity and the method of generalized functions, a generalized solution to the problem is constructed under the action of non-stationary force loads and various types of heat sources. Regular integral representations of generalized solutions are obtained for given initial temperature, displacements and velocity of the rod. Using the Mathcad program, numerical calculations of the Green's tensor for a system with dimensionless thermoelastic parameters are carried out. Solutions to Cauchy problems under the action of force loads and heat sources distributed along the rod are given