In this paper, we investigate dynamical mass generation in (2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in Tc-Nf space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature.