The purpose of the research is to construct the method of the boundary integral equations (BIEM) for solving a transient value problem of coupled thermoelastodynamics. The following problems have been solved: (i)) the influence of the temperature on the character of distribution of thermoelastic waves was investigated; (ii) The thermoelastic statement of media in two-and three-dimensional cases was considered under by action of the non-stationary concentrated mass forces and thermal sources; (iii) Two types of Tensors of fundamental stresses were constructed, their properties were investigated, and their asymptotics were constructed; (iv) the dynamical analogue of Formula of Gauss. The BIEM for the thermostresses condition of media was developed at the given non-stationary loadings and thermal flow on its border in bounds in two-and three-dimensional cases.