<p>We provide a review of recent works in thermoelasticity theory. Using the boundary state method (BSM) for constructing numerical-analytical solutions of problems by means of computing systems supporting “computer algebras” is recommended. The structures of Hilbert spaces of internal and boundary states of a thermoelastostatic medium (TE) are established and the method for describing inner products of both isomorphic spaces is developed. A technique of saving computational resources while performing the procedure of orthogonalization of bases of separable spaces is discovered. When solving problems of thermoelasticity theory coupled/uncoupled by boundary conditions (BC), it is unnecessary to decompose them into a traditional sequence of temperature and elastic problems. A classification of TE problems is given. Calculations are performed and the results are discussed for two classes of problems.</p>