We discuss the renormalization prescription for fermions at finite temperature and describe the procedure for calculating radiative corrections. Novel features arise, such as a lack of explicit Lorentz invariance, 1k2 singularities, and the absorption of soft photons from the background heat bath. The methods are illustrated by explicit calculation of the electron renormalization and the radiative corrections to H-->e+e- (with H being spin zero) in finite-temperature QED.