  We derive a spectral representation for the two-point Green function for
arbitrary composite field operators in Thermo Field Dynamics (TFD). A simple
way for calculating the spectral density within TFD is pointed out and compared
with known results from the imaginary time formalism. The method is applied to
hot $\phi^4$ theory. We give a compact derivation of the one-loop contribution
to the shear viscosity and show that it is dominated by low-momentum plasmons.
