  We investigate the full counting statistics of extreme-near-field radiative
heat transfer using nonequilibrium Green's function formalism. In the extreme
near field, the electron-electron interactions between two metallic bodies
dominate the heat transfer process. We start from a general tight-binding
electron Hamiltonian and obtain a Levitov-Lesovik like scaled cumulant
generating function (SCGF) using random phase approximation to deal with
electron-electron interaction. The expressions of heat current and its
fluctuation (second cumulant) are obtained from the SCGF. The fluctuation
symmetry relation of the SCGF is verified. In the linear response limit (small
temperature gradient), we express the heat current cumulant by a linear
combination of lower order cumulants. The heat current fluctuation is $2k_B
T^2$ times the thermal conductance with $T$ the average temperature in the
linear response limit, and this provides an evaluation of heat current
fluctuation by measuring the thermal conductance in extreme-near
field-radiative heat transfer.
