  Ultraluminous X-ray sources (ULXs) are mainly powered by accretion in neutron
stars or stellar-mass black holes. Accreting at rates exceeding the Eddington
limit by factors of a few up to hundreds, radiation pressure is expected to
inflate the accretion disc, and drive fast winds that have in fact been
observed at significant fractions of the speed of light. Given the
super-Eddington luminosity, the accretion disc will be thicker than in
sub-Eddington accretors such as common active galactic nuclei and X-ray
binaries, leading to a different spectral energy distribution and, possibly, a
different thermal status of the wind. Here we show the first attempt to
calculate the photoionization balance of the winds driven by strong radiation
pressure in thick discs with a focus on ULXs hosting black holes or
non-magnetic neutron stars. We find that the winds are generally in thermally
stable equilibrium, but long-term variations in the accretion rate and the
inclination due to precession may have significant effects on the wind
appearance and stability. Our model trends can explain the observed correlation
between the spectral residuals around 1 keV and the ULX spectral state. We also
find a possible correlation between the spectral hardness of the ULX, the wind
velocity and the ionization parameter in support of the general scenario.
