The calculation of the massless fermion damping rate to order g2T in t
he long-wavelength limit of hot gauge theories using the recently deve
loped resummation methods in terms of hard thermal loops is reviewed.
Ward identities between the effective propagators and vertices are use
d to formally prove the gauge independence of the damping rate to this
order in a wide class of gauges. We also discuss some aspects of the
cutoff dependence of the gauge-dependent terms proportional to the mas
s-shell condition.