What is the relationship between a white dwarf and black dwarf?

No longer emitting heat or light, the white dwarf will become a black dwarf. Because it emits no radiation, it is nearly impossible to see. However, the black dwarf would still retain its mass, allowing scientists to detect the effects produced by its gravitational field.

Explanation:

white dwarfs are hot, black dwarfs are cold

Explanation:

a white dwarf is a slowly burning and aging corpse of a main sequence star such as our sun. they are up to 40 times hotter then the sun, ranking among one of the hottest objects in the universe, except their luminosity is so low that all their heat stays in them basically forever.

On the other hand, a black dwarf is a theoretical ending to a white dwarf, over the course of trillions of years, white dwarfs cool down into black dwarfs. black dwarfs rank among the coldest possible temperature. We aren't sure if these are really a thing, because we still haven't given white dwarfs enough time to cool down.