We apply our recently suggested statistical approach to thermal evolution of isolated neutron stars and accreting quasistationary neutron stars in X-ray transients for constraining the position and relative broadening \alpha of the direct Urca threshold of powerful neutrino emission in neutron star cores . We show that most likely explanation of observations corresponds to \alpha \approx 0.08 - 0.10 and to the neutron star mass , at which the direct Urca process is open , M _ { D } \approx 1.6 - 1.8 { M } \odot .