If you really, really had a large neutron star -- just a smidgen short of what would be required to turn it into a black hole -- then might we enter a new regime? Specifically, imagine a neutron decaying, releasing a neutrino (or antineutrino, whatever). If the escape velocity for the star is larger than the velocity of that neutrino (which will be damn near lightspeed) then one could argue that in a sense, neutron decay has now become impossible. Anyhow, cooling via the mechanism of neutron decay / re-synthesis cycle (where neutrinos released in both cases) is now impossible. So: new regime for neutron stars. However... I believe this actually cannot happen, because I think that the escape velocity for a stable neutron star cannot be brought arbitrarily near lightspeed -- if you try, then it'd collapse once it reached some threshold like 0.6c, or something like that. In which case, this "new regime" is the empty set.