  We analyze observations of the mass profiles of 175 late-type galaxies in the
Spitzer Photometry \& Accurate Rotation Curves (SPARC) database to construct
the temperature profile of their dark matter (DM) halos by assuming that (1) DM
in the halos obeys either the Fermi-Dirac or the Maxwell-Boltzmann
distribution, and (2) the halos are in the virial state. We derive the
dispersion velocity of DM at the center of the halos and show that its
correlation with the halo's total mass is the same as the one estimated in
N-body simulations. The correlation is also the same as the observed relation
between the two variables for visible matter in galaxies. Taking the latter
agreement as a validation of our analysis, we derive the mass to the
temperature of DM at the edge of the halos and show that it is galaxy
independent and is equal to $m/T_R\simeq 10^{10}$ in natural units. Since the
analyzed galaxies are far away in the sky, we conclude that DM is a thermal
relic, and $T_R$ in the above ratio can be expressed in terms of the
temperature of the cosmic microwave background (CMB) at the time of DM
decoupling. This result is used to study possible cosmological scenarios. We
show that observations are at odds with (1) non-thermal DM, (2) hot DM, and (3)
collision-less cold DM. Our findings are in favor of a warm DM with a mass of
$\sim 1\,$MeV.
