  We construct the gauge invariant fermion correlator in the Schwinger model on
the torus. At zero temperature, this correlator falls off with a rate given by
the Coulomb energy of an infinitely heavy charge. At high temperature, the
screening mass approaches $\pi T/2$, and this in the presence of a mass gap.
The fractional Matsubara frequency arises from the action of a pair of induced
merons at high temperature that are localized over a range on the order of the
meson Compton wavelength $1/m=\sqrt{\pi}/g$. We discuss the quenched
approximation in this model, and comment on the possible relevance of some of
these results to higher dimensions.
