An analysis of the compatibility of Cattaneo-Vernotte’s constitutive equation for the heat flux density vector with the hypothesis of local thermodynamic equilibrium is presented. This compatibility is checked by determining the entropy production rate per unit volume. In fact, within the scheme of local equilibrium, Clausius’ inequality implies that the entropy production rate must be non-negative. The evaluation of the entropy production rate is performed for a solid slab which experiences a sudden change of the boundary temperature and for a semi-infinite solid with a time-varying boundary heat flux. A domain of non-stationary phenomena is found in which Cattaneo-Vernotte’s equation is compatible with the assumption of local equilibrium and yields results definitely different from those predicted by Fourier’s equation.