  We explore the thermal evolution of a neutron star undergoing episodes of
intense accretion, separated by long periods of quiescence. By using an exact
cooling code we follow in detail the flow of heat in the star due to the
time-dependent accretion-induced heating from pycno-nuclear reactions in the
stellar crust, to the surface photon emission, and the neutrino cooling. These
models allow us to study the neutron stars of the Soft X-Ray Transients. In
agreement with Brown, Bildsten and Rutledge (1998) we conclude that the soft
component of the quiescent luminosity of Aql X-1, 4U 1608-522, and of the
recently discovered SAX J1808.4, can be understood as thermal emission from a
cooling neutron star with negligible neutrino emission. However, we show that
in the case of Cen X-4, despite its long recurrence time, strong neutrino
emission from the neutron star inner core is necessary to understand the
observed low ratio of quiescent to outburst luminosity. This result implies
that the neutron star in Cen X-4 is heavier than the one in the other systems
and the pairing critical temperature in its center must be low enough (well
below 10^9 K) to avoid a strong suppression of the neutrino emission.
