  We explore, using an exact cooling code, the thermal evolution of a neutron
star undergoing episodes of intense accretion, alternated by long periods of
quiescence (e.g. Soft X-Ray Transients). We find that the soft component of the
quiescent luminosity of Aql X-1, 4U 1608-522 and of SAX J1808.4-3658 can be
understood as thermal emission from a cooling neutron star with negligible
neutrino emission. In the case of Cen X-4 strong neutrino emission from the
inner core is necessary to explain the observation: this may indicate that the
neutron star of Cen X-4 is heavier than 1.4 Msun. This study opens the
possibility of using the quiescent emission of Soft X-Ray Transients as a tool
for probing the core superfluidity in relation to the mass of the neutron star.
