The existence of the high mass pulsars PSR J1614-2230 and PSR J0348-0432 with masses of about 2 M_sun requires a sufficiently stiff equation of state (EoS) of the stellar matter to fulfill this constraint. We succeeded to explain the thermal evolution of compact stars with stiff hadronic EoS in the framework of the ``nuclear medium cooling" scenario. We have also investigated the case when due to phase transition to quark matter the third family of compact stars for higher densities can exist. In this case high-mass twin stars could show different cooling behavior. The cooling scenarios have a discriminating power for selection of optimal EoS models for compact stars.
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