  Finite temperature modifies the running of the QCD coupling alpha_s(k,T) with
resolution k. After calculating the thermal quark and gluon masses
selfconsistently, we determine the quark-quark and quark-gluon cross sections
in the plasma based on the running coupling. We find that the running coupling
enhances these cross sections by factors of two to four depending on the
temperature. We also compute the energy loss dE/dx of a high-energy quark in
the plasma as a function of temperature. Our study suggests that, beside
t-channel processes, inverse Compton scattering is a relevant process for a
quantitative understanding of the energy loss of an incident quark in a hot
plasma.
