  In accreting neutron star X-ray transients, the neutron star crust can be
substantially heated out of thermal equilibrium with the core during an
accretion outburst. The observed subsequent cooling in quiescence (when
accretion has halted) offers a unique opportunity to study the structure and
thermal properties of the crust. Initially crust cooling modelling studies
focussed on transient X-ray binaries with prolonged accretion outbursts (> 1
year) such that the crust would be significantly heated for the cooling to be
detectable. Here we present the results of applying a theoretical model to the
observed cooling curve after a short accretion outburst of only ~10 weeks. In
our study we use the 2010 outburst of the transiently accreting 11 Hz X-ray
pulsar in the globular cluster Terzan 5. Observationally it was found that the
crust in this source was still hot more than 4 years after the end of its short
accretion outburst. From our modelling we found that such a long-lived hot
crust implies some unusual crustal properties such as a very low thermal
conductivity (> 10 times lower than determined for the other crust cooling
sources). In addition, we present our preliminary results of the modelling of
the ongoing cooling of the neutron star in MXB 1659-298. This transient X-ray
source went back into quiescence in March 2017 after an accretion phase of ~1.8
years. We compare our predictions for the cooling curve after this outburst
with the cooling curve of the same source obtained after its previous outburst
which ended in 2001.
