  (Abridged). The type-I X-ray bursting low mass X-ray binary KS 1731-260 was
recently detected for the first time in quiescence by Wijnands et al.,
following an approximately 13 yr outburst which ended in Feb 2001. Unlike all
other known transient neutron stars, the duration of this recent outburst is as
long as the thermal diffusion time of the crust. The large amount of heat
deposited by reactions in the crust will have heated the crust to temperatures
much higher than the equilibrium core temperature. As a result, the thermal
luminosity currently observed from the neutron star is dominated not by the
core, but by the crust. Moreover, the level and the time evolution of quiescent
luminosity is determined mostly by the amount of heat deposited in the crust
during the most recent outburst. Using estimates of the outburst mass accretion
rate, our calculations of the quiescent flux immediately following the end of
the outburst agree with the observed quiescent flux to within a factor of a
few. We present simulations of the evolution of the quiescent lightcurve for
different scenarios of the crust microphysics, and demonstrate that monitoring
observations (with currently flying instruments) spanning from 1--30 yr can
measure the crust cooling timescale and the total amount of heat stored in the
crust. These quantities have not been directly measured for any neutron star.
