  We study heat transfer between conductors, mediated by the excitation of a
monomodal harmonic oscillator. Using a simple model, we show that the onset of
rectification in the system is directly related to the nonlinearity of the
electron gas dispersion relation. When the metals have strictly linear
dispersion relation a Landauer type expression for the thermal current holds,
symmetric with respect to the temperature difference. Rectification becomes
prominent when deviations from linear dispersion exist, and the fermionic model
cannot be mapped into a harmonic- bosonized- representation. The effects
described here are relevant for understanding radiative heat transfer and
vibrational energy flow in electrically insulating molecular junctions.
