  We present Rossi X-Ray Timing Explorer and Swift observations made during the
final three weeks of the 2006-2007 outburst of the super-Eddington neutron star
(NS) transient XTE J1701-462, as well as Chandra and XMM-Newton observations
covering the first ~800 days of the subsequent quiescent phase. The source
transitioned quickly from active accretion to quiescence, with the luminosity
dropping by over 3 orders of magnitude in ~13 days. The spectra obtained during
quiescence exhibit both a thermal component, presumed to originate in emission
from the NS surface, and a non-thermal component of uncertain origin, which has
shown large and irregular variability. We interpret the observed decay of the
inferred effective surface temperature of the NS in quiescence as the cooling
of the NS crust after having been heated and brought out of thermal equilibrium
with the core during the outburst. The interpretation of the data is
complicated by an apparent temporary increase in temperature ~220 days into
quiescence, possibly due to an additional spurt of accretion. We derive an
exponential decay timescale of ~120 (+30/-20) days for the inferred temperature
(excluding observations affected by the temporary increase). This short
timescale indicates a highly conductive NS crust. Further observations are
needed to confirm whether the crust is still slowly cooling or has already
reached thermal equilibrium with the core at a surface temperature of ~125 eV.
The latter would imply a high equilibrium bolometric thermal luminosity of
~5x10^{33} erg/s for an assumed distance of 8.8 kpc.
