  It is shown, in the framework of the Thomas-Fermi model at finite
temperature, that a cooling non-degenerate gas of massive neutrinos will, at a
certain temperature, become unstable and undergo a first-order phase transition
in which quasi-degenerate supermassive neutrino stars are formed through
gravitational collapse. For neutrinos in the mass range of 10 to 25
keV/c$^{2}$, these compact dark objects could mimic the role of supermassive
black holes that are reported to exist at the centres of galaxies and
quasi-stellar objects.
