ABSTRACT 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.