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 $R = 15.2km$.

8 pages, 8 figures, minor changes to match published version