In this paper, the boundary value problems of the linear theory of thermoelasticity of binary mixtures are investigated by means of the potential method (boundary integral method). The basic properties of thermoelastopotentials are treaded. The uniqueness and existence theorems of solutions of the interior and exterior boundary value problems by means potential method and multidimensional singular integral equations are proved. The Sommerfeld-Kupradze type radiation conditions are established. The existence of eigenfrequencies of the interior homogeneous boundary value problems of steady oscillations is studied.