  We examine the thermal evolution of a sequence of compact objects containing
low-mass hadronic and high-mass quark-hadronic stars constructed from a
microscopically motivated equation of state. The dependence of the cooling
tracks in the temperature versus age plane is studied on the variations of the
gaplessness parameter (the ratio of the pairing gap for red-green quarks to the
electron chemical potential) and the magnitude of blue quark gap. The pairing
in the red-green channel is modeled assuming an inhomogeneous superconducting
phase to avoid tachionic instabilities and anomalies in the specific heat; the
blue colored condensate is modeled as a Bardeen-Cooper-Schrieffer (BCS)-type
color superconductor. We find that massive stars containing quark matter cool
faster in the neutrino-cooling era if one of the colors (blue) is unpaired
and/or the remaining colors (red-green) are paired in a inhomogeneous gapless
superconducting state. The cooling curves show significant variations along the
sequence, as the mass (or the central density) of the models is varied. This
feature provides a handle for fine-tuning the models to fit the data on the
surface temperatures of same-age neutron stars. In the late-time photon cooling
era we observe inversion in the temperature arrangement of models, i.e., stars
experiencing fast neutrino cooling are asymptotically hotter than their slowly
cooling counterparts.
