  At zero temperature, the Lorentz invariance is strictly preserved in
three-dimensional quantum electrodynamics. This property ensures that the
velocity of massless fermions is not renormalized by the gauge interaction. At
finite temperature, however, the Lorentz invariance is explicitly broken by the
thermal fluctuation. The longitudinal component of gauge interaction becomes
short-ranged due to thermal screening, whereas the transverse component remains
long-ranged because of local gauge invariance. The transverse gauge interaction
leads to singular corrections to the fermion self-energy and thus results in an
unusual renormalization of the fermion velocity. We calculate the renormalized
fermion velocity $v^R(p_0,\mathbf{p},T)$ by employing a renormalization group
analysis, and discuss the influence of the anomalous dimension $\eta_n$ on the
fermion specific heat.
