When the sun becomes a white dwarf why will it take SO long to cool off?

In article , Radium wrote:
I've read about the sun's life cycle. Apparently, when the sun becomes
a white dwarf, it will take at least a trillion years to completely
cool off. Why such a long time?

It's heavy and it's hot, but it's only got a small surface area
to radiate it's heat through. So, to allow the heat out through that
small area is going to take a long time.

It seems that the sun would exist much longer dead [i.e. as a white
dwarf] than alive [burning hydrogen and helium].

White dwarfs aren't dead. They're not producing any new energy
(by conversion of mass through fusion), but they've got a *lot* of
stored energy in both thermal and heat forms ; they've got quite
considerable rotational energy; and many of them have significant
magnetic fields too. All these are signs of something non-dead.
When a white dwarf has radiated it's thermal energy to the point
that it's internal convection is too slow to maintain a magnetic field
and it's just a dark (well, IR-radiating) body with considerable mass
and rotation, then it's a black dwarf. And it's lifetime as that is in
the order of 10^20 times as long as the present age of the universe.
Assuming that protons are long-term unstable. Which is not accepted, let
alone proven.

--
Aidan Karley, FGS
Aberdeen, Scotland
Written at Sat, 19 Aug 2006 16:43 +0100, but posted later.