  If the inflaton is a heavy scalar field, it may equilibrate slower than some
other degrees of freedom, e.g. non-Abelian gauge bosons. In this case,
perturbations in the inflaton field and in a thermal plasma coexist from a
given moment onwards. We derive a gauge-invariant set of three coupled
equations governing the time evolution of such a system. Despite singular
coefficients, a reliable numerical solution can be obtained for a long time
period, starting from phase oscillations inside the Hubble horizon, and
extending until acoustic oscillations in a radiation-dominated universe.
Benchmarks are illustrated from a ``weak regime'', where perturbations have a
quantum-mechanical origin but get dissipated by interactions with the plasma.
Among applications of our formalism could be inhomogeneity-induced nucleations
in post-inflationary phase transitions, and the production of scalar-induced
gravitational waves.
