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...
