  Recent experimental measurements for near-field radiative heat transfer
between two bodies have been able to approach the gap distance within $2 \;
\textrm{nm}$, where the contributions of Coulomb fluctuation and electron's
tunneling are comparable. Using the nonequilibrium Green's function method in
the $G_{0}W_{0}$ approximation, based on a tight-binding model, we obtain for
the energy current a Caroli formula from the Meir-Wingreen formula in the local
equilibrium approximation. Also, the Caroli formula is consistent with the
evanescent part of the heat transfer from the theory of fluctuational
electrodynamics. We go beyond the local equilibrium approximation to study the
energy transfer in the crossover region from electron tunneling to Coulomb
fluctuation based on a numerical calculation.
