************************************************************************* 72033 Recent re-analysis of archival ASCA observations of three transiently accreting neutron stars (Cen X-4, Aql X-1, and 4U 1608--52) suggests that some of the quiescent emission is powered by the heated core. Accretion may still contribute to the quiescent luminosity. Variability provides a discriminant between these two sources of thermal surface emission. We propose to re-observe these objects while they are in quiescence. This, combined with the archival ASCA data, will allow us to search for variability, on timescales of weeks to years, in the quiescent luminosities and spectra. The proposed observations will also provide benchmarks for future observations with, e.g., AXAF and XMM. *************************************************************************