  We calculate the thermal structure and quiescent thermal luminosity of
accreting neutron stars (warmed by deep crustal heating in accreted matter) in
soft X-ray transients (SXTs). We consider neutron stars with nucleon and
hyperon cores and with accreted envelopes. It is assumed that an envelope has
an outer helium layer (of variable depth) and deeper layers of heavier
elements, either with iron or with much heavier nuclei (of atomic weight A >
100) on the top (Haensel & Zdunik 1990, 2003, astro-ph/0305220). The relation
between the internal and surface stellar temperatures is obtained and fitted.
The quiescent luminosity of the hottest (low-mass) and coldest (high-mass)
neutron stars is calculated, together with the ranges of its possible
variations due to variable thickness of the helium layer. The results are
compared with observations of SXTs, particularly, containing the coldest (SAX
J1808.4-3658) and the hottest (Aql X-1) neutron stars. The observations of SAX
J1808.4-3658 in a quiescent state on March 24, 2001 (Campana et al. 2002,
astro-ph/0206376) can be explained only if this SXT contains a massive neutron
star with a nucleon/hyperon core; a hyperon core with a not too low fraction of
electrons is preferable. Future observations may discriminate between the
various models of hyperon/nucleon dense matter. The thermal emission of SAX
J1808.4-3658 is also sensitive to the models of plasma ionization in the
outermost surface layers and can serve for testing such models.
