  The gap equation for fermions in a version of thermal QED in three dimensions
is studied numerically in the Schwinger-Dyson formalism. The interest in this
theory has been recently revived since it has been proposed as a model of
high-temperature superconductors. We include wave-function renormalization in
our equations and use a non-bare vertex. We then have to solve a system of two
integral equations by a relaxation algorithm. Fermion and photon self-energies
varying independently with energy and momentum are used, which should produce
more accurate results than in the previous literature. The behaviour of the
theory with increasing temperature and number of fermion flavours is then
carefully analyzed.
