  The central compact object in the supernova remnant HESS J1731-347 appears to
be the hottest observed isolated cooling neutron star. The cooling theory of
neutron stars enables one to explain observations of this star by assuming the
presence of strong proton superfluidity in the stellar core and the existence
of the surface heat blanketing envelope which almost fully consists of carbon.
The cooling model of this star is elaborated to take proper account of the
neutrino emission due to neutron-neutron collisions which is not suppressed by
proton superfluidity. Using the results of spectral fits of observed thermal
spectra for the distance of 3.2 kpc and the cooling theory for the neutron star
of age 27 kyr, new constraints on the stellar mass and radius are obtained
which are more stringent than those derived from the spectral fits alone.
