  Static thermal equilibrium of a quantum self-gravitating ideal gas in general
relativity is studied at any temperature, taking into account the
Tolman-Ehrenfest effect. Thermal contribution to the gravitational stability of
static neutron cores is quantified. The curve of maximum mass with respect to
temperature is reported. At low temperatures the Oppenheimer-Volkoff
calculation is recovered, while at high temperatures the recently reported
classical gas calculation is recovered. An ultimate upper mass limit $M =
2.43M_\odot$ of all maximum values is found to occur at Tolman temperature $ T
= 1.27mc^2$ with radius $R = 15.2km$.
