My understanding is that a black hole large enough to be colder than the CMB will grow (gain more mass energy by absorbing CMB photons, even in "empty" space, than it loses by Hawking radiation), continuing to cool.

I assume but am not sure that the cooling of an already-sufficiently-cold black hole in this manner is slower than the cooling of the CMB itself due to expansion, so that at some point as the universe winds down it will begin to shrink again and eventually evaporate, but definitely over the lifetime of any star we see a black hole this side won't radiate significantly, or evaporate.