In this paper we consider an elastic homogeneous isotropic indefinite medium, in a region of which general external forces and sources of heat are distributed. With a suitable proceeding we reduced the problem of integration of relative thermoelastic equations to the determination of two vectors, a scalar function and the temperature which satisfy determined differential equations. In the particular case in which the linear thermal coefficient of dilatation is sufficiently small that we can neglect the terms which contain the square of it, we have assigned, of the above equations, any solutions, with definite integrals, by means of known retarded potentials and with the introduction of new functions that we called thermoelastic potentials.