  We present a new 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 that has high effective temperature, and it is
consistent with the cooling without exotic phases. The observation also gives
the mass range of $M \geqslant 1.5 M_\odot$, which may conflict with the
current plausible cooling scenario of compact stars. There are some cooled
compact stars such as Vela or 3C58, which can be barely explained by the
minimal cooling scenario, which includes the neutrino emission by nucleon
superfluidity (PBF). Therefore, we invoke the exotic cooling processes, where a
heavier star cools faster than lighter one. However, the scenario seems to be
inconsistent with the observation of Cas A. Therefore, we present a new cooling
scenario to explain the observation of Cas A by constructing models that
include a quark color superconducting (CSC) phase with a large energy gap; this
phase appears at ultrahigh density region and reduces neutrino emissivity. In
our model, a compact star has CSC quark core with a low neutrino emissivity
surrounded by high emissivity region made by normal quarks. We present cooling
curves obtained from the evolutionary calculations of compact stars: while
heavier stars cool slowly, and lighter ones indicate the opposite tendency
without considering nucleon superfluidity. Furthermore, we show that our
scenario is consistent with the recent observations of the effective
temperature of Cas A during the last 10 years, including nucleon superfluidity.
