  The presence of radiatively driven outflows is well established in
ultraluminous X-ray sources (ULXs). These outflows are optically thick and can
reprocess a significant fraction of the accretion luminosity. Assuming
isotropic emission, escaping radiation from the outflow's photosphere has the
potential to irradiate the outer disc. Here, we explore how the atmosphere of
the outer disc would respond to such irradiation, and specifically whether
unstable heating may lead to significant mass loss via thermally-driven winds.
We find that, for a range of physically relevant system parameters, this mass
loss may actually switch off the inflow entirely and potentially drive
limit-cycle behaviour (likely modulated on the timescale of the outer disc). In
ULXs harbouring neutron stars, magnetic fields tend to have a slight
destabilizing effect; for the strongest magnetic fields and highest accretion
rates, this can push otherwise stable systems into the unstable regime. We
explore the prevalence of the instability in a simulated sample of ULXs
obtained from a binary population synthesis calculation. We find that almost
all neutron star and black hole ULXs with Eddington-scaled accretion rates of
$\dot{m}_0 < 100$ should be able to drive powerful outflows from their outer
discs. Several known ULXs are expected to lie in this regime; the persistence
of accretion in these sources implies the irradiation may be anisotropic which
can be reconciled with the inferred reprocessed (optical) emission if some of
this originates in the wind photosphere or irradiation of the secondary star.
