  A linear irreversible thermodynamic framework of heat conduction in rigid
conductors is introduced. The deviation from local equilibrium is characterized
by a single internal variable and a current intensity factor. A general
constitutive evolution equation of the current density of the internal energy
is derived by introducing linear relationship between the thermodynamic forces
and fluxes. The Fourier, Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys
type and Green-Naghdi type equations of heat conduction are obtained as special
cases. The universal character of the approach is demonstrated by two examples.
Solutions illustrating the properties of the equation with jump boundary
conditions are given.
