We investigate the simultaneous presence of topological and thermal disorde
r in amorphous silicon. We find that localized electronic states are very s
ensitive to moderate amounts of thermal disorder: for a given gap or band t
ail electronic eigenstate, both the fraction of the total charge on a given
site as well as the energy eigenvalue can vary greatly with small (thermal
ly accessible) changes to the positions of the atoms. This observation, whi
ch is almost certainly relevant to any disordered insulator including glass
es, has important implications to the microscopic theory of transport, opti
cal properties, and doping, as well as existing models of defect kinetics.