Would the surface temperature. of stars classified as white dwarfs be generally higher or lower than that of stars classified as supergiants?

The temperature of the white dwarf is the residual temperature left from the star's nova; it can start very high (around 100,000K) but will gradually drop as the star enters the white dwarf stage of evolution because it is no longer undergoing any fusion reactions and is therefore not producing any energy.

You could have a white dwarf at, say, 5 K. Once it reaches 2-3K, it is called a black dwarf, though none exist or will exist for trillions of years. As long as it is warmer than the background temperature of space (2–3K), it is classified as a white dwarf.

A red super giant has a temperature of about 4000K, which is much lower than our sun and about the same as the coolest known white dwarf. A blue supergiant would have a temperature of about 20,000 K. The temperature of a supergiant would depend on the color of the star.

A white dwarf can therefore be hotter than the hottest supergiant or colder than the coldest supergiant. Hence, the temperature range of a white dwarf would be from 4 K up to about 100,000 K. To cover all supergiants, you would be looking at 4000 K to say 50,000 K.

Our sun is approximately 6,000 K in comparison.

The surface temperature of stars classified as white dwarfs is generally higher than that of stars classified as supergiants.