  Monitoring the cooling of neutron-star crusts heated during accretion
outbursts allows us to infer the physics of the dense matter present in the
crust. We examine the crust cooling evolution of the low-mass X-ray binary MXB
1659-29 up to ~505 days after the end of its 2015 outburst (hereafter outburst
II) and compare it with what we observed after its previous 1999 outburst
(hereafter outburst I) using data obtained from the Swift, XMM-Newton, and
Chandra observatories. The observed effective surface temperature of the
neutron star in MXB 1659-29 dropped from ~92 eV to ~56 eV from ~12 days to ~505
days after the end of outburst II. The most recently performed observation
after outburst II suggests that the crust is close to returning to thermal
equilibrium with the core. We model the crust heating and cooling for both its
outbursts collectively to understand the effect of parameters that may change
for every outburst (e.g., the average accretion rate, the length of outburst,
the envelope composition of the neutron star at the end of the outburst) and
those which can be assumed to remain the same during these two outbursts (e.g.,
the neutron star mass, its radius). Our modelling indicates that all parameters
were consistent between the two outbursts with no need for any significant
changes. In particular, the strength and the depth of the shallow heating
mechanism at work (in the crust) were inferred to be the same during both
outbursts, contrary to what has been found when modelling the cooling curves
after multiple outburst of another source, MAXI J0556-332. This difference in
source behaviour is not understood. We discuss our results in the context of
our current understanding of cooling of accretion-heated neutron-star crusts,
and in particular with respect to the unexplained shallow heating mechanism.
