  We present a general framework for studying strongly coupled radiative and
conductive heat transfer between arbitrarily shaped bodies separated by
sub-wavelength distances. Our formulation is based on a macroscopic approach
that couples our recent fluctuating volume--current (FVC) method of near-field
heat transfer to the more well known Fourier conduction transport equation. We
apply our technique to consider heat exchange between aluminum-zinc oxide
nanorods and show that the presence of bulk plasmon resonances can result in
extremely large radiative heat transfer rates (roughly twenty times larger than
observed in planar geometries), whose interplay with conductive transport leads
to nonlinear temperature profiles along the nanorods.
