  In this paper, we extend our earlier one loop analysis to two loops and give
a simple diagrammatic description for the retarded Greens functions at finite
temperature, in terms of forward scattering amplitudes of on-shell thermal
particles. We present a simple discussion, which can be easily generalized to
any field theory, of the temperature dependent parts of the retarded two and
three point functions in scalar field theory and QED. As an application of our
result at two loops, we show how the infrared singularities in the thermal part
of the retarded photon self-energy, cancel in QED_2 in the limit of vanishing
electron mass.
