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 = 2.43 M _ { \odot } of all maximum values is found to occur at Tolman temperature T = 1.27 mc ^ { 2 } with radius R = 15.2 km .