  We consider the partition functions of QCD and QED at high temperature
assuming small coupling constants, and present arguments in favor of an
improved perturbative expansion in terms of unstable excitations. Our effective
propagators are derived from spectral functions with a constant width. These
spectral functions describe screening and damping of gluons (photons) as well
as ``Brownian'' motion of quarks (electrons). BRST-invariance allows us to
reduce the number of independent width parameters to three. These are
determined in a self-consistent way from the one-loop self energy and
polarization tensor in the infrared limit thus rendering this limit finite. All
spectral width parameters are found to be proportional to $g T$. We reproduce
the well known expression for the electric ``Debye''-screening mass. The
transverse (magnetic) gluons (photons) are found to interact only at nonzero
momentum or energy, at least to leading order. As a consequence their spectral
function acquires a width only away from the infrared limit. Finally, plasmon
modes are determined and found to be strongly damped.
