(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.
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