A linear relaxation equation for the heat flux in a fluid, proposed by Vernotte as a generalization of Fourier's law, is shown for liquids to be consistent with the assumption that thermal energy is carried by elastic waves of very high frequency which may be envisaged as being propagated in a continuum. The elastic constants and the velocity of the waves are obtained from the infinite frequency limits of viscoelastic equations, derived in earlier papers to describe the relaxation of compressional and shearing strains, and from these, the relaxation time and thermal conductivity are calculated for several nonassociated liquids with the aid of a theory of Debye. It is shown that the Vernotte equation may be viewed formally, from the point of view of irreversible thermodynamics, as a force‐flux equation linking two irreversible processes, and this interpretation makes it possible to calculate terms in the pressure and internal energy which are nonlinear in the temperature gradient.