Neutron stars are held up by neutron degeneracy pressure, btw, not electron degeneracy pressure. White dwarfs stars are held up by that (even though they can be very hot; the temperature needed to "lift" degeneracy increases with the mass of the object.) Even the cores of some very large stars are electron degenerate; this is why they remain stable against the "pair production instability": there aren't any states into which newly created electrons can go, suppressing pair production.