Final answer:
White dwarfs can be very hot but have low luminosity due to their small surface area and high surface temperatures. These dying stars emit light from the heat represented by the motions of the atomic nuclei in their interior.
Step-by-step explanation:
White dwarfs can be both very hot and have very low luminosity due to their small total surface area and high surface temperatures. These stars have a small radius, which means they have a small surface area to emit light from. Even though each square meter on a white dwarf puts out a lot of energy, the overall star appears dim because it has a limited surface area.
For example, the nearby star 40 Eridani B is a white dwarf with a surface temperature of 12,000 K. Despite its high temperature, its luminosity is only 1/275 that of the Sun. This is because its radius is only 1.4% that of the Sun, resulting in a small surface area.
As white dwarfs are dying stars, they have reached the end of their productive lives and are ready for their stories to be over. They continue to emit light from the heat represented by the motions of the atomic nuclei in their interior, but gradually, they radiate away all their heat into space.