Cooling of a rotating strange star in the color superconducting phase with a crust

Aims. We investigate the thermal evolution of strange stars in the 2-flavor color superconductivity and color-flavor locked phases under the influence of deconfinement heating. Methods. Due to the spin-down of strange stars, the nuclear matter at the base of the thin crusts dissolves into quarks, releasing energy to heating the stars. On the other hand, the neutrino emissivities and specific heat involving pairing quarks are suppressed by the large pairing gap in color superconducting phases. Then the thermal evolution equation of strange stars is calculated. Results. Deconfinement heating delays the cooling of strange stars considerably. The presence of color superconductivity with a large gap enhances this effect. Especially, in the color-flavor locked phase, the stars cannot be very cold at an early age but they cool slowly. For the stars with strong magnetic fields, a significant heating period could exist during the first several ten or hundred years. In addition, we reckoned that a possible theoretical limit line, which is determined by the competition between deconfinement heating and surface photon cooling, may indicate the upper limit temperature that isolated compact stars should not exceed. Conclusions. Deconfinement heating is important for the thermal evolution of strange stars and is especially determinant for the stars in color-flavor locked phase which could show characteristic cooling behavior under this heating effect.