  Nuclear reactions occurring deep in the crust of a transiently accreting
neutron star efficiently maintain the core at a temperature >5e7 K. When
accretion halts, the envelope relaxes to a thermal equilibrium set by the flux
from the hot core, as if the neutron star were newly born. For the
time-averaged accretion rates typical of low-mass X-ray transients, standard
neutrino cooling is unimportant and the core thermally re-radiates the
deposited heat. The resulting luminosity has the same magnitude as that
observed from several transient neutron stars in quiescence. Confirmation of
this mechanism would strongly constrain rapid neutrino cooling mechanisms for
neutron stars. Thermal emission had previously been dismissed as a predominant
source of quiescent emission since blackbody spectral fits implied an emitting
area much smaller than a neutron star's surface. However, as with thermal
emission from radio pulsars, fits with realistic emergent spectra will imply a
substantially larger emitting area. Other emission mechanisms, such as
accretion or a pulsar shock, can also operate in quiescence and generate
intensity and spectral variations over short timescales. Indeed, quiescent
accretion may produce gravitationally redshifted metal photoionization edges in
the quiescent spectra (detectable with AXAF and XMM). We discuss past
observations of Aql~X-1 and note that the low luminosity X-ray sources in
globular clusters and the Be star/X-ray transients are excellent candidates for
future study.
