  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.
