  We study how interacting localized degrees of freedom are affected by slow
thermal fluctuations that change the effective local disorder. We compute the
time-averaged (annealed) conductance in the insulating regime and find three
distinct insulating phases, separated by two transitions. The first occurs
between a non-resonating insulator and an intermittent metal. The average
conductance is always dominated by rare temporal fluctuations. However, in the
intermittent metal, they are so strong that the system becomes metallic for an
exponentially small fraction of the time. A second transition occurs within
that phase. At stronger disorder, there is a single optimal path providing the
dominant contribution to the conductance at all times, but closer to
delocalization, a transition to a phase with fluctuating paths occurs. This
last phase displays the quantum analogon of configurational chaos in glassy
systems in that thermal fluctuations induce significant changes of the dominant
decay channels. While in the insulator the annealed conductance is strictly
bigger than the conductance with typical, frozen disorder, we show that the
threshold to delocalization is insensitive to whether or not thermal
fluctuations are admitted. This rules out a potential bistability, at fixed
disorder, of a localized phase with suppressed internal fluctuations and a
delocalized, internally fluctuating phase.
