We formulate thermoelastic problem of rational design of plain composite structures with uniformly stressed reinforcement. The structures are subjected to successive loading by two independent systems of stationary loads. We present a qualitative analysis of corresponding system of constitutive equations and boundary conditions. We develop a method of iterative solution of such problems. This method belongs to the class of methods of perturbation theory and it allows us to `split’ the coupled subproblems of determination of parameters of rational reinforcement, the temperature fields, and stress-strain state of the structure. We discuss particular analytic and numerical solutions. Based on these examples, we relationships between variation of structure of reinforcement and stress-strain state, on the one hand, and the level of heat effect, mass loading, and materials, on the other hand. We reveal a possibility of existence of two solutions of such problems caused by substantial nonlinearity of static boundary conditions.