The stability of isothermal dark matter halos has been widely studied before. In this paper, we investigate the stability of non-isothermal fermionic dark matter halos. We show that in the presence of temperature gradient, the force due to the pressure has both inward and outward components. In some regions of halos, the inward force that provides stability is due to the pressure rather than gravity. Moreover, it is shown that higher temperature gradients lead to halos with lower mass and size. We prove that if the temperature is left as a free positive profile, one can place no phase-space lower bound on the mass of dark matter. For halos that are in the low degeneracy classic domain, we derive an analytic expression of their temperature in terms of their mass density and place an upper bound on the mass of dark matter by requiring that temperature is not negative. We then use the Burkert mass profile for the Milky Way to show that if the central temperature of the halo is a few Kelvins, the mass of dark matter cannot exceed a few keV.