We have recently shown that, as a compact star containing mixed-phase matter slows down, the compression can cause deconfinement phase transition, and thus enhance the chemical deviations and raise the chemical heating eiYiciency. In a previous study, only the direct Urca processes in nucleon and quark matter were considered. In this work, we extend the previous analysis to the case where the much slower modified Urca processes operate in nucleon matter. We find a fast promotion in the surface effective temperature of hybrid stars, and that the cooling process is dominated by both the nucleon and quark channels.
