Observations of accreting neutron star transients in quiescence offer an excellent probe of the temperature of the deep crust and core. I shall discuss how well the measured thermal emission, when combined with information on the time-averaged accretion and calculations of thermal transport in the crust, can constrain the neutrino emissivity of the core. For the best-studied object, Aql X-1, the measured surface temperature and spin can constrain whether a steady-state r-mode is present, as suggested recently by Wagoner.