I tended to think that under electron degeneracy, electrons are spread over more energy states instead of being spread over so much space, so the exclusion principle lets more electrons to be effectively collocated. So making a white dwarf hotter would perhaps make the white dwarf (of unchanged mass) shrink by electrons going into even more different energy states, most of them fully packed.
Now I encountered a rather different explanation: cold electrons are big due to the uncertainty principle.
(Anders Sandberg's answer has pointed out that white dwarfs don't actually shrink! While the degenerate core, or at least it central part, increases in density, the outer non-degenerate regions expand and the star expands as a whole which is directly observable. However, the question about what is happening in the middle of the star remains.)
If translated to actual physics, are the two explanations/mechanisms somehow the same one? And if not, which one contributes quantitatively more of the effect that a hotter white dwarf of the same mass is denser in the middle, in the equilibrium state?
(My own background: I am not a physicist. I understand what makes atoms occupy a volume but I don't understand how the "size" of a mere electron is even defined when trying to "fully pack" an energy level or a single quantum state of electrons within some space. I'm also well aware that white dwarfs are far from composed of only electrons but I am not sure whether all that hadronic matter plays any role in how tightly I can pack the electrons themselves.)