  We compute the power spectrum of super-horizon curvature perturbations
generated during a late period of thermal inflation, taking into account
fluctuation-dissipation effects resulting from the scalar flaton field's
interactions with the ambient radiation bath. We find that, at the onset of
thermal inflation, the flaton field may reach an equilibrium with the radiation
bath even for relatively small coupling constants, maintaining a spectrum of
thermal fluctuations until the critical temperature $T_c$, below which thermal
effects stop holding the field at the false potential minimum. This enhances
the field variance compared to purely quantum fluctuations, therefore
increasing the average energy density during thermal inflation and damping the
induced curvature perturbations. In particular, we find that this inhibits the
later formation of primordial black holes, at least on scales that leave the
horizon for $T>T_c$. The larger thermal field variance also reduces the
duration of a period of fast-roll inflation below $T_c$, as the field rolls to
the true potential minimum, which should also affect the generation of (large)
curvature perturbations on even smaller scales.
