  We compute the radiative heat transfer between two sheets of 2D Dirac
materials, including topological Chern insulators and graphene, within the
framework of the local approximation for the optical response of these
materials. In this approximation, which neglects spatial dispersion, we derive
both numerically and analytically the short-distance asymptotic of the
near-field heat transfer in these systems, and show that it scales as the
inverse of the distance between the two sheets. Finally, we discuss the
limitations to the validity of this scaling law imposed by spatial dispersion
in 2D Dirac materials.
