Aims. We aim to extract the transmission spectrum of the HI Balmer lines of the ultra-hot Jupiter (UHJ) KELT-20b/MASCARA-2b from observations and to further compare the results with what was obtained through forward modelling, accounting for non-local thermodynamic equilibrium (NLTE) effects. Methods. We extracted the line profiles from six transits obtained with the HARPS-N high-resolution spectrograph attached to the Telescopio Nazionale Galileo telescope. We computed the temperature-pressure (TP) profile employing the HELIOS code in the lower atmosphere and the CLOUDY NLTE code in the middle and upper atmosphere. We further used CLOUDY to compute the theoretical planetary transmission spectrum in LTE and NLTE for comparison with observations. Results. We detected the Hα (0.79±0.03%; 1.25 R_p), Ηβ (0.52±0.03%; 1.17 R_p), and Ηγ (0.39±0.06%; 1.13 R_p) lines, and we detected the Ηδ line at almost 4σ (0.27±0.07%; 1.09 R_p). The models predict an isothermal temperature of ≈2200 K at pressures >10⁻² bar and of ≈7700 K at pressures <10⁻⁸ bar, with a roughly linear temperature rise in between. In the middle and upper atmosphere, the NLTE TP profile is up to ~3000 K hotter than in LTE. The synthetic transmission spectrum derived from the NLTE TP profile is in good agreement with the observed HI Balmer line profiles, validating our obtained atmospheric structure. Instead, the synthetic transmission spectrum derived from the LTE TP profile leads to significantly weaker absorption compared to the observations. Conclusions. Metals appear to be the primary agents leading to the temperature inversion in UHJs, and the impact of NLTE effects on them increases the magnitude of the inversion. We find that the impact of NLTE effects on the TP profile of KELT-20b/MASCARA-2b is larger than for the hotter UHJ KELT-9b, and thus NLTE effects might also be relevant for planets cooler than KELT-20b/MASCARA-2b.