The thermoelastic problem is stated for the case of equistressed plane composite structures reinforced by fibers of constant cross-sectional area. In the operation process, structures undergo a set of successive independent steady state thermal and forced loads. We perform the qualitative analysis of a corresponding system of governing equations and boundary conditions and propose an interaction procedure for solving such problems. As a result, we can split out the total system of equations and find the solution to the following independent sub-problems: (1) determination of parameters for the rational (optimal) reinforcement; (2) determination of temperature fields; (3) determination of the stress-strain states in the components of the structure. We obtain the analytical solutions for the problem in asymptotic approach and for the one-dimensional problem in the case of elongated rectangular plates. Based on these solutions, we arrive at the conclusion that the solution to the problem under consideration is non-unique. This non-uniqueness can be explained by the fact that the static boundary conditions under consideration are of strong nonlinear type.