  A pseudoscalar inflaton $\varphi$, coupled to the topological charge density
$F\tilde{F}$ of a non-Abelian sector, can decay to gauge bosons ($\varphi\to g
g $), which may thermalize rapidly. The friction felt by $\varphi$ is then
increased by non-Abelian "strong sphalerons", leading to a self-amplifying
process that can efficiently heat up the medium. We determine a lower bound for
the gravitational wave production rate from such a process, originating via
hydrodynamic fluctuations and particle collisions, in terms of a minimal number
of parameters. Only a moderate fraction of energy density is converted to
gravitational waves, suggesting that non-Abelian models may avoid the
overproduction observed in some Abelian cases.
