Effective electron temperature (red solid line) and X-ray photon index Γ (dashed blue line) as a function of the half-opening angle of the accretion disc funnel, as predicted by the model of Madau & Haardt (2024). The model accounts for coronal cooling due to inverse-Compton scattering of disc photons, which becomes increasingly efficient at high accretion rates, where the disc is geometrically thicker and the funnel correspondingly narrower. In this regime, the enhanced soft-photon flux leads to stronger cooling of the coronal plasma, resulting in progressively steeper hard X-ray spectra with increasing Eddington ratios. Details of the calculations are provided in Appendix A.