  We write down the gap equation for the fermion self-energy in a
finite-temperature abelian gauge theory in three dimensions. The instantaneous
approximation is relaxed, momentum-dependent fermion and photon self-energies
are considered, and the corresponding Schwinger-Dyson equation is solved
numerically. The relation between the zero-momentum and zero-temperature
fermion self-energy and the critical temperature T_c, above which there is no
dynamical mass generation, is then studied. We also investigate the effect
which the number of fermion flavours N_f has on the results, and we give the
phase diagram of the theory with respect to T and N_f.
