  We show that within a recently developed nonlocal, chiral quark model the
critical densities for a phase transition to color superconducting quark matter
under neutron star conditions can be low enough that these phases occur in
compact star configurations with masses below 1.4 M_sun. We study the cooling
of these objects in isolation for different values of the gravitational mass
and thus different composition and structure of the interior. Our equation of
state allows for a 2SC phase with a large quark gap Delta ~ 100 MeV for u and d
quarks of two colors, a normal quark matter phase and their coexistence in a
mixed phase within the hybrid star interior. We argue that, if the phases with
unpaired quarks were allowed, the corresponding hybrid stars would cool too
fast to describe the neutron star cooling data existing by today. We
incorporate other attractive channels permitting a weak pairing of the residual
quarks which remained unpaired in the 2SC phase and demonstrate that the model
does not contradict the cooling data if the weak pairing gaps are of the order
of 0.1 MeV.
