  The exact solutions for linear cosmological perturbations which have been
obtained for collisionless relativistic matter within thermal field theory are
extended to a self-interacting case. The two-loop contributions of scalar
$\lambda\phi^4$ theory to the thermal graviton self-energy are evaluated, which
give the $O(\lambda)$ corrections in the perturbation equations. The changes
are found to be perturbative on scales comparable to or larger than the Hubble
horizon, but the determination of the large-time damping behavior of subhorizon
perturbations requires a resummation of thermally induced masses.
