  A non-Fourier thermal transport regime characterizes the heat conduction in
solids with internal structure. Several thermodynamic theories attempt to
explain the separation from the Fourier regime in such kind of systems. Here we
develop a two temperature model to describe the non-Fourier regime from the
principles of non-equilibrium thermodynamics. The basic assumption is the
existence of two well separated length scales in the system, namely, one
related with the matrix dimension (bulk) and the other with the characteristic
length of the internal structure. Two Fourier type coupled transport equations
are obtained for the temperatures which describe the heat conduction in each of
the length scales. Recent experimental results from several groups on the
thermal response of different structured materials are satisfactorily
reproduced by using the coupling parameter as a fitting parameter. The
similarities and differences of the present formalism with other theories are
discussed.
