Assuming that the accretion disk has been totally consumed by the black hole, does the temperature of the black hole due to Hawking radiation vary with respect with proximity with the black hole? For example, if I were next to the black hole, would this radiation would have a higher temperature than I was far away? Should the temperature gradient, in effect, be corrected for gravitational redshift, such that the temperature declines as distance from the blackhole's center decreases? Or should the temperature gradient not get corrected for the gravitational redshift, such that the temperature of the blackhole at some location is determined by the local observer at its local coordinate frame, rather than from a global coordinate frame of reference? If light cannot escape beyond the black hole's event horizon. Doesn't that make it a heat sink? If it is a heat sink, musn't that mean that, as far as thermodynamics are concerned, that it must be treated as a colder body, and not a hotter one, so a black hole does not have infinite temperature and entropy? Also, wouldn't an evaporating black hole be evaporating due to the universe heating it up?