  Dynamical mass generation in a three-dimensional version of
finite-temperature QED is studied with the help of Schwinger-Dyson equations in
the real-time formalism. We go beyond the bare-vertex approximation and include
wave-function renormalization effects. This introduces a system of two integral
equations which are solved numerically. In order to increase the reliability of
the results, fermion and photon self-energies varying independently with energy
and momentum are used. The method applied enables a detailed study of the
behaviour of the theory with increasing temperature and number of fermion
flavours.
