  We present a formulation for a local cooling function to be employed in the
diffuse, hot corona region of 3D GRMHD simulations of accreting black holes.
This new cooling function calculates the cooling rate due to inverse Compton
scattering by considering the relevant microphysics in each cell in the corona
and approximating the radiation energy density and Compton temperature there by
integrating over the thermal seed photon flux from the disk surface. The method
either assumes ion and electron temperatures are equal (1T), or calculates them
separately (2T) using an instantaneous equilibrium approach predicated on the
actual relevant rate equations (Coulomb and Compton). The method is shown to be
consistent with a more detailed ray-tracing calculation where the bulk of the
cooling occurs, but is substantially less costly to perform. As an example, we
apply these methods to a \textsc{harm3d} simulation of a $10 M_\odot$,
non-spinning black hole, accreting at nominally 1\% the Eddington value. Both
1T and 2T approaches lead to increased radiative efficiency and a larger
fraction of total cooling in the corona as compared to the original
target-temperature cooling function used by \textsc{harm3d}, especially in the
1T case. Time-averaged post-processing reveals that the continuum spectral
observations predicted from these simulations are qualitatively similar to
actual X-ray binary data, especially so for the 1T approach which yields a
harder power-law component ($\Gamma = 2.25$) compared to the 2T version
($\Gamma = 2.53$)
