  In anticipation of a subsequent application to QCD, we consider the case of
QED at high temperature. We introduce a Fradkin representation into the exact,
Schwingerian, functional expression of a fermion propagator, as well as a new
and relevant version of the Bloch-Nordsieck (BN) model, which extracts the soft
contributions of every perturbative graph, in contradistinction to the assumed
separation of energy scales of previous semi-perturbative treatments. Our
results are applicable to the absorption of a fast particle which enters a heat
bath, as well as to the propagation of a symmetric pulse within the thermal
medium due to the appearance of an instantaneous, shock-wave-like source acting
in the medium. An exponentially-decreasing time dependence of the incident
particle's initial momentum combines with a stronger decrease in the particle's
energy, estimated by a sum over all Matsubara frequencies, to model an initial
"fireball", which subsequently decays in a Gaussian fashion. When extended to
QCD, qualitative applications could be made to RHIC scattering, in which a
fireball appears, expands and is damped away.
