even though a white dwarf may burn hot, it's size is what limitsit's luminosity. Here is one way to look at it: Imagine a whitedwarf with the mass of our sun. Our sun's surface temp is rightaround 5,770K and weighs one solar mass. Now, this imaginary whitedwarf would be about the size of the earth and have a surface tempof around 10,000K - 11,000K. This white dwarf would have a surfacearea 1/333,000 of the sun. A white dwarf of this size is aboutaverage and as you can imagine, has very little room to put outenergy compared to other solar masses.