* White dwarfs cool down: White dwarfs are the remnants of stars like our Sun after they exhaust their nuclear fuel. They are incredibly dense and hot, but they don't have a source of energy to keep them hot forever. Over billions and billions of years, they slowly cool down and dim.
* Black dwarf: Eventually, a white dwarf will cool down to the point where it no longer emits any significant light or heat. This hypothetical stage is called a black dwarf. It's important to note that the universe isn't old enough for any black dwarfs to exist yet.
* Time scales: The process of a white dwarf cooling to a black dwarf is estimated to take trillions of years. This is far longer than the current age of the universe.
In short: The Sun will become a white dwarf, but it won't stay that way forever. It will continue to cool down over an incredibly long time, eventually becoming a black dwarf.