  Transient LMXBs that host neutron stars (NSs) provide excellent laboratories
for probing the dense matter physics present in NS crusts. During accretion
outbursts in LMXBs, exothermic reactions may heat the NS crust, disrupting the
crust-core equilibrium. When the outburst ceases, the crust cools to restore
thermal equilibrium with the core. Monitoring this evolution allows us to probe
the dense matter physics in the crust. Properties of the deeper crustal layers
can be probed at later times after the end of the outburst. We report on the
unexpected late-time temperature evolution (>2000 days after the end of their
outbursts) of two NSs in LMXBs, XTE J1701-462 and EXO 0748-676. Although both
these sources exhibited very different outbursts (in terms of duration and the
average accretion rate), they exhibit an unusually steep decay of ~7 eV in the
observed effective temperature (occurring in a time span of ~700 days) around
~2000 days after the end of their outbursts. Furthermore, they both showed an
even more unexpected rise of ~3 eV in temperature (over a time period of
~500-2000 days) after this steep decay. This rise was significant at the
2.4{\sigma} and 8.5{\sigma} level for XTE J1701-462 and EXO 0748-676,
respectively. The physical explanation for such behaviour is unknown and cannot
be straightforwardly be explained within the cooling hypothesis. In addition,
this observed evolution cannot be well explained by low-level accretion either
without invoking many assumptions. We investigate the potential pathways in the
theoretical heating and cooling models that could reproduce this unusual
behaviour, which so far has been observed in two crust-cooling sources. Such a
temperature increase has not been observed in the other NS crust-cooling
sources at similarly late times, although it cannot be excluded that this might
be a result of the inadequate sampling obtained at such late times.
