  We describe HEROIC, an upgraded version of the relativistic radiative
post-processor code HERO described in a previous paper, but which now Includes
Comptonization. HEROIC models Comptonization via the Kompaneets equation, using
a quadratic approximation for the source function in the short characteristics
radiation solver. It employs a simple form of accelerated lambda iteration to
handle regions of high scattering opacity. In addition to solving for the
radiation field, HEROIC also solves for the gas temperature by applying the
condition of radiative equilibrium. We present benchmarks and tests of the
Comptonization module in HEROIC with simple 1D and 3D scattering problems. We
also test the ability of the code to handle various relativistic effects using
model atmospheres and accretion flows in a black hole space-time. We present
two applications of HEROIC to general relativistic MHD simulations of accretion
discs. One application is to a thin accretion disc around a black hole. We find
that the gas below the photosphere in the multi-dimensional HEROIC solution is
nearly isothermal, quite different from previous solutions based on 1D plane
parallel atmospheres. The second application is to a geometrically thick
radiation-dominated accretion disc accreting at 11 times the Eddington rate.
The multi-dimensional HEROIC solution shows that, for observers who are on axis
and look down the polar funnel, the isotropic equivalent luminosity could be
more than ten times the Eddington limit, even though the spectrum might still
look thermal and show no signs of relativistic beaming.
