  Conventional wisdom is that increasing temperature causes quantum coherence
to decrease. Using finite temperature perturbation theory and exact
calculations for the strongly correlated bosonic Mott insulating state we show
a practical counter-example that can be explored in optical lattice
experiments: the short-range coherence of the Mott insulating phase can
increase substantially with increasing temperature. We demonstrate that this
phenomenon originates from thermally produced defects that can tunnel with
ease. Since the near zero temperature coherence properties have been measured
with high precision we expect these results to be verifiable in current
experiments.
