40}$]{} keV. We found no significant improvement by leaving the column density ${N_{\textrm{H}}}$, the covering factor ${\textrm{C}_{\textrm{F}}}$, or the photon index free to vary among the different observations. The best-fitting parameters are reported in Table \[tab:fits\_4388\], while the contour plots of the cut-off energy and photon index are shown in Fig. \[fig:cont\_cutoffpl\]. We also tried to include a reflection component, replacing the cut-off power law with [[pexrav]{}]{} and leaving the reflection fraction ${\mathcal{R}}$ free and tied among the observations. The fit is not improved and we obtain only an upper limit ${\mathcal{R}}< 0.12$. We note that the large equivalent width of the [Fe K$\alpha$]{} line is consistent with that reported by [@kamraj2017], who suggest the presence of a large amount of Compton-thin line-emitting material.

Then, we fitted the data using a more physical Comptonisation model. We replaced the cut-off power law with [[compps]{}]{}, assuming a spherical geometry ($\textsc{geom}=0$). We assumed a seed photon temperature of 100 eV. Fixing this parameter at other values, like 10 eV, does not alter the results significantly. We fitted for the electron temperature ${kT_{\textrm{e}}}$ and the Compton parameter $y = 4\tau ({kT_{\textrm{e}}}/m_{\textrm{e}} c^2)$. We chose to use the Compton parameter instead of the optical depth 