  Radiative heat transfer (RHT) between macroscopic bodies at separations that
are much smaller than the thermal wavelength is ruled by evanescent
electromagnetic modes and can be orders of magnitude more efficient than its
far-field counterpart, which is described by the Stefan-Boltzmann law. In this
Letter we present a microscopic theory of RHT in van der Waals stacks
comprising graphene and a natural hyperbolic material, i.e. hexagonal boron
nitride (hBN). We demonstrate that RHT between hot carriers in graphene and
hyperbolic phonon-polaritons in hBN is extremely efficient at room temperature,
leading to picosecond time scales for the carrier cooling dynamics.
