We present 3D radiation hydrodynamics simulations of common-envelope (CE) evolution involving a 12 solar mass red supergiant donor and a 3 solar mass companion. Existing 3D simulations are predominantly adiabatic, focusing strongly on low-mass donors on the red giant and asymptotic giant branches. However, the adiabatic assumption breaks down once the perturbed CE material becomes optically thin or when entering a longer-timescale evolutionary phase after the dynamical plunge-in. This is especially important for high-mass red supergiant donors, which have short thermal timescales, adding significant uncertainty in understanding how massive binary stars evolve into gravitational-wave sources, X-ray binaries, stripped-envelope supernovae, and more. We compare our radiation hydrodynamics simulations with an adiabatic simulation from Paper I that is otherwise identical, finding that radiative diffusion strongly inhibits CE ejection. The fraction of ejected mass is roughly half that of the adiabatic case when recombination energy release is not included. Almost no material is ejected during the dynamical plunge-in, and longer-timescale ejection during the slow spiral-in is suppressed. However, the orbital separation reached at the end of the dynamical plunge-in does not differ significantly. The large amount of remaining bound mass tentatively supports the emerging view that the dynamical plunge-in is followed by a non-adiabatic phase, during which a substantial fraction of the envelope is ejected and the binary orbit may continue to evolve.