Changes in Fourier’s equation on heat propagation have been proposed by C. Cattaneo and G. Grioli. In this work we generalize these modifications and propose a theory on the propagation of thermomechanical waves, by means of which the paradox of the infinite propagation velocity is avoided. We consider only isentropic deformations of the continuum (as this seems to agree with experimental results) and use the theory of iterated discontinuities. The law of propagation of the thermomechanical waves is determined by the purely mechanical aspect of the problem considered here.