  We study the effect of asymmetric fermionic dark matter (DM) on the thermal
evolution of neutron stars (NSs). No interaction between DM and baryonic matter
is assumed, except the gravitational one. Using the two-fluid formalism, we
show that DM accumulated in the core of a star pulls inwards the outer baryonic
layers of the star, increasing the baryonic density in the NS core. As a
result, it significantly affects the star's thermal evolution by triggering an
early onset of the direct Urca process and modifying the photon emission from
the surface caused by the decrease of the radius. Thus, due to the
gravitational pull of DM, the direct Urca process becomes kinematically allowed
for stars with lower masses. Based on these results, we discuss the importance
of NS observations at different distances from the Galactic center. Since the
DM distribution peaks towards the Galactic center, NSs in this region are
expected to contain higher DM fractions that could lead to a different cooling
behavior.
