  We investigate the renormalizability of the classical $\phi^4$ theory at
finite temperature. We calculate the time-dependent two point function to two
loop order and show that it can be rendered finite by the counterterms of the
classical static theory. As an application the classical plasmon damping rate
is found to be $\gamma = \lambda^2 T^2/1536 \pi m$. When we use the high
temperature expression for $m$ given by dimensional reduction, the rate is
found to agree with the quantum mechanical result.
