We discuss the correlation function of hadronic currents in the Schwin
ger model at finite temperature T. We explicitly construct the retarde
d correlator in real time and obtain analytical results for the euclid
ean correlator on a torus. Both constructions lead to the same finite
temperature spectral function. The spatial screening lengths in the me
sonic channels are related to the dynamical meson mass m = e/root pi a
nd not 2 pi T even in the infinite temperature limit. The relevance of
our results for the finite temperature problem in four dimensions is
discussed.