  Under the combination effect of the recommencement heating due to spin-down
of strange stars and the heat perseveration due to weak conduct heat of the
crust, the Cooper pair breaking and formation(PBF) in color superconduction
quark matter arises. We investigated the cooling of the strange stars with a
crust in color superconductivity phase including both decomfinement heating and
PBF process. We find that deconfinement heating can delay the thermal evolution
of strange stars and the PBF process suppresses the early temperature rise of
the stars. The cooling strange stars behave within the brightness constraint of
young compact objects when the color superconductivity gap is small enough.
