  The traditional approach to studying near-field thermal transfer is based on
fluctuational electrodynamics. However, this approach may not be suitable for
nonequilibrium states due to dynamic drivings. In our work, we introduce a
theoretical framework to describe the phenomenon of near-field heat transfer
between two objects when subjected to periodic time modulations. We utilize the
machinery of nonequilibrium Green's function to derive general expressions for
the DC energy current in Floquet space. Furthermore, we also obtain the energy
current under the condition of small driving amplitude. The external drivings
create a nonequilibrium state, which gives rise to various effects such as
heat-transfer enhancement, heat-transfer suppression, and cooling. To
illustrate these phenomena, we conduct numerical calculations on a system of
Coulomb-coupled quantum dots, and specifically investigate the scenario of
periodically driving electronic reservoir. In our calculations, we employ the
$G_0W_0$ approximation, which does not require self-consistent iteration and is
suitable for weak Coulomb interaction. Our theoretical formalism can be applied
to study near-field energy transfer between two metallic plates under periodic
time modulations.
