  We perform a theoretical study of the near-field heat transfer between two
atomically thin metallic layers, isolated galvanically but coupled by the
Coulomb interaction, within the framework of fluctuational electrodynamics in
the Coulomb limit. We clarify the role of disorder and spatial dispersion, and
identify several distinct regimes of the heat transfer. We find that the
plasmon contribution to the heat current is suppressed both in the clean and
diffusive limits, but dominates in a parametrically wide crossover region at
sufficiently high temperatures.
