Final answer:
A white dwarf that has cooled down to near absolute zero is known as a black dwarf, not a brown dwarf, and it represents a white dwarf that has radiated away all its thermal energy.
Step-by-step explanation:
The term you're looking for is a black dwarf, which is a theoretical astronomical object representing a white dwarf that has cooled down to a temperature near absolute zero, emitting no light or heat. This is different from a brown dwarf, which is an object intermediate in size between a planet and a star that is capable of deuterium fusion but not hydrogen fusion. Unlike brown dwarfs, a black dwarf would have no fusion processes occurring within it, essentially making it a stellar remnant that has used up all its thermal energy.