  We have monitored the transient neutron star low-mass X-ray binary 1RXS
J180408.9-342058 in quiescence after its ~4.5 month outburst in 2015. The
source has been observed using Swift and XMM-Newton. Its X-ray spectra were
dominated by a thermal component. The thermal evolution showed a gradual X-ray
luminosity decay from ~18 x 10^32 to ~4 x 10^32 (D/5.8 kpc)^2 erg s^{-1}
between ~8 and ~379 d in quiescence, and the inferred neutron star surface
temperature (for an observer at infinity; using a neutron star atmosphere
model) decreased from ~100 to ~71 eV. This can be interpreted as cooling of an
accretion-heated neutron star crust. Modelling the observed temperature curve
(using NSCOOL) indicated that the source required ~1.9 MeV per accreted nucleon
of shallow heating in addition to the standard deep crustal heating to explain
its thermal evolution. Alternatively, the decay could also be modelled without
the presence of deep crustal heating, only having a shallow heat source (again
~1.9 MeV per accreted nucleon was required). However, the XMM-Newton data
statistically required an additional power-law component. This component
contributed ~30 per cent of the total unabsorbed flux in 0.5-10 keV energy
range. The physical origin of this component is unknown. One possibility is
that it arises from low-level accretion. The presence of this component in the
spectrum complicates our cooling crust interpretation because it might indicate
that the smooth luminosity and temperature decay curves we observed may not be
due to crust cooling but due to some other process.
