  We present Chandra and XMM-Newton X-ray observations that monitor the neutron
star cooling of the quasi-persistent neutron star X-ray transients KS 1731-260
and MXB 1659-29 for approximately 4 years after these sources returned to
quiescence from prolonged outbursts. In both sources the outbursts were long
enough to significantly heat the neutron star crust out of thermal equilibrium
with the core. We analyse the X-ray spectra by fitting absorbed neutron star
atmosphere models to the observations. The results of our analysis strengthen
the preliminary findings of Wijnands et al. that in both sources the neutron
star crust cools down very rapidly suggesting it has a high heat conductivity
and that the neutron star core requires enhanced core cooling processes.
Importantly, we now detect the flattening of the cooling in both sources as the
crust returns to thermal equilibrium with the core. We measure the thermal
equilbrium flux and temperature in both sources by fitting a curve that decays
exponentially to a constant level. The cooling curves cannot be fit with just a
simple exponential decay without the constant offset. We find the constant
bolometric flux and effective temperature components to be (9.2 +/- 0.9)E-14
ergs/cm^2/s and 70.0 +/- 1.6 eV in KS 1731-260 and (1.7 +/- 0.3)E-14
ergs/cm^2/s and 51.6 +/- 1.4 eV in MXB 1659-29. In addition, we find that the
crust of KS 1731-260 cools faster than that of MXB 1659-29 by a factor of ~2,
likely due to different crustal properties. This is the first time that the
cooling of a neutron star crust into thermal equilibrium with the core has been
observed in such detail.
