  We discuss the color-superconductivity and its effect on the cooling behavior
of strange quark stars. The neutrino emissivity and specific heat of quark
matter are calculated within the BCS theory. In the superconducting phase, the
emissivity decreases and causes suppression of the cooling rate. It is shown
that the phase transition leads to a sudden discontinuous suppression of the
cooling rate in cooperation with the specific heat.
