  We study long-term thermal evolution of neutron stars in soft X-ray
transients (SXTs), taking the deep crustal heating into account consistently
with the changes of the composition of the crust. We collect observational
estimates of average accretion rates and thermal luminosities of such neutron
stars and compare the theory with observations. We perform simulations of
thermal evolution of accreting neutron stars, considering the gradual
replacement of the original nonaccreted crust by the reprocessed accreted
matter, the neutrino and photon energy losses, and the deep crustal heating due
to nuclear reactions in the accreted crust. We test and compare results for
different modern theoretical models. We update a compilation of the
observational estimates of the thermal luminosities in quiescence and average
accretion rates in the SXTs and compare the observational estimates with the
theoretical results. Long-term thermal evolution of transiently accreting
neutron stars is nonmonotonic. The quasi-equilibrium temperature in quiescence
reaches a minimum and then increases toward the final steady state. The
quasi-equilibrium thermal luminosity of a neutron star in an SXT can be
substantially lower at the minimum than in the final state. This enlarges the
range of possibilities for theoretical interpretation of observations of such
neutron stars. The updates of the theory and observations leave unchanged the
previous conclusions that the direct Urca process operates in relatively cold
neutron stars and that an accreted heat-blanketing envelope is likely present
in relatively hot neutron stars in the SXTs in quiescence. The results of the
comparison of theory with observations favor suppression of the triplet pairing
type of nucleon superfluidity in the neutron-star matter.
