We have derived analytic approximations of neutrino luminosities and heat capacities of neutron stars for different leading neutrino mechanisms and superfluidity models in neutron star cores. The approximate expressions depend on stellar mass and radius. They are valid for a wide class of nucleonic EOSs, and they can greatly simplify an analysis of thermal states of isolated and accreting neutron stars. For the former, we have also derived approximate cooling curves valid at both neutrino and photon cooling stages. Using these results, we have analyzed possible thermal states of the neutron star RX J1856.5-3754 and shown that they likely correspond to the neutrino cooling enhanced by neutron superfluidity. For accreting neutron stars in X-ray transients, we have analysed their quasi-stationary internal thermal states.

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