  We show a scenario for the cooling of compact stars considering the central
source of Cassiopeia A (Cas A). The Cas A observation shows that the central
source is a compact star with high effective temperature, and it is consistent
with the cooling without exotic phases. The Cas A observation also gives the
mass range of $M \geq 1.5 M_\odot$. It may conflict with the current cooling
scenarios of compact stars that heavy stars show rapid cooling. We include the
effect of the color superconducting (CSC) quark matter phase on the thermal
evolution of compact stars. We assume the gap energy of CSC quark phase is
large ($\Delta \gtrsim \mathrm{10 MeV}$), and we simulate the cooling of
compact stars. We present cooling curves obtained from the evolutionary
calculations of compact stars: while heavier stars cool slowly, and lighter
ones indicate the opposite tendency.
