What is the temperature range of a black dwarf star?
A black dwarf is what would be left (hypothetically) when a white dwarf lost all it's energy. Therefore the energy would be zero and the temperature would be the same as space, 2-3 degrees K. As the is no energy being generated (white dwarfs do not generated heat anymore they just slowly lose it into space), the range would be zero.
The existence of black dwarfs is completely hypothetical as it is estimated that it will take over a trillion years for a star to completely cool, and the universe isn't even 14 billion years old yet. The oldest known white dwarfs are about 11 billion years and they are still around 3000 degrees.