  The natural transition from the radiative regime to the conductive regime of
heat transfer between two identical isotropic dielectric solid materials, is
questioned by investigating the possibility of induced phonon transfer in
vacuum. We describe the process in a general way assuming a certain phonon
coupling mechanism between the two identical solids, then we particularly
illustrate the case of coupling through Casimir force. We analyze how this
mechanism of heat transfer compares and competes with the near field thermal
radiation using a local model of the dielectric function. We show that the
former mechanism can be very effective and even overpass the latter mechanism
depending on the nature of the solid dielectric materials, the distance gap
between them as well as the operating temperature regime.
