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We use the Stefan-Boltzmann law to derive and investigate what we will call the black hole CMB temperature luminosity. Interestingly, the CMB luminosity is always the same for every black hole at a luminosity distance equal to the Schwarzschild radius, which is fully valid in black hole cosmology, a topic that is actively discussed to this day. The CMB black hole luminosity is always the same , regardless of the mass of the black hole. This is in contrast to the Bekenstein-Hawking luminosity, which is linked to the Hawking temperature, that is mass dependent.
Haug et al. (Fri,) studied this question.