  Thermal states of neutron stars in soft X-ray transients (SXRTs) are thought
to be determined by "deep crustal heating" in the accreted matter that drives
the quiescent luminosity and cooling via emission of photons and neutrinos from
the interior. In this study, we assume a global thermal steady-state of the
transient system and calculate the heating curves (quiescent surface luminosity
as a function of mean accretion rate) predicted from theoretical models, taking
into account variations in the equations of state, superfluidity gaps,
thickness of the light element layer and a phenomenological description of the
direct Urca threshold. We further provide a statistical analysis on the
uncertainties in these parameters, and compare the overall results with
observations of several SXRTs, in particular the two sources containing the
coldest (SAX J1808.4-3658) and the hottest (Aql X-1) neutron stars.
Interpretation of the observational data indicates that the direct Urca process
is required for the most massive stars and also suggests small superfluid gaps.
