  We monitored the quiescent thermal emission from neutron stars in low-mass
X-ray binaries after active periods of intense activity in x-rays (outbursts).
The theoretical modeling of the thermal relaxation of the neutron star crust
may be used to establish constraints on the crust composition and transport
properties, depending on the astrophysical scenarios assumed. We numerically
simulated the thermal evolution of the neutron star crust and compared them
with inferred surface temperatures for five sources: MXB 1659-29, KS 1731-260,
EXO 0748-676, XTE J1701-462 and IGR J17480-2446. We find that the evolution of
MXB 1659-29, KS 1731-260 and EXO 0748-676 can be well described within a deep
crustal cooling scenario. Conversely, we find that the other two sources can
only be explained with models beyond crustal cooling. For the peculiar emission
of XTE J1701-462 we propose alternative scenarios such as residual accretion
during quiescence, additional heat sources in the outer crust, and/or thermal
isolation of the inner crust due to a buried magnetic field. We also explain
the very recent reported temperature of IGR J17480-2446 with an additional heat
deposition in the outer crust from shallow sources.
