Re: Core temperature @loyal commenter
I think you will find that the core temperature of a white dwarf is anything but equal to the surface temperature. I have not done the math on this, and I have only backed up my initial thoughts on the matter to the wikipedia article on white dwarfs, but it is quite simple.
1. If they are isothermic or close to it and you a have surface that is a few thousand Kelvin the radiation will be quite high as that is not far from an active star. Of course in total quite a lot less since the surface area is a lot smaller. But the heat capacity simply isn't big enough to keep this running for billions of years with a core temperature that is the same, even with it's big mass.
2. If the core at an active star is several million degrees and the surface only a few thousand, why would that change when it collapses after fusion stops?
Anyhow, white dwarf interior physics is not my specialty, but I find this bit from the wiki article not to contradict my limited understanding:
Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore almost isothermal, and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.
So you are right it being isothermic, just that is has an atmosphere/surface that is not.
Its cold outside, there's no kind of atmosphere,
I'm all alone, more or less.
Let me fly, far away from here,
Fun, fun, fun, In the sun, sun, sun
*As for the original question what does 5000 times cooler mean, the closest I got was in total radiation. If you ignore the to the power of four bit in black body radiation you get that it's surface is about one ten thousandth and the temperature is about half.