English: "The peaks at z ≈ 7 and 3 are due to H and He reionization, respectively. The thermal evolution is in good agreement with observations of the Ly α forest. Data points are based on measurements of absorption line widths as a function of strength (Schaye et al. 2000; Hiss et al. 2018; Rorai et al. 2018; Telikova, Shternin & Balashev 2019; Gaikwad et al. 2020), on the small-scale cut-off in the flux power spectrum (Boera et al. 2019; Walther et al. 2019), or on both types of methods (Gaikwad et al. 2021)." "At z > 3 (z > 7.2) Ploeckinger & Schaye (2020) attenuate the Faucher-Giguère (2020) spectrum above the H i (He ii) ionization energies using H i (He ii) column densities tuned to match the effective photo-ionization and photo-heating rates that Faucher-Giguère (2020) finds to be needed to match observations of the optical depth seen by the CMB and observations of the intergalactic medium. In the models used to compute the cooling rates, hydrogen and helium reionize at z = 7.8 and z = 3.5, respectively. To account for the extra heat due to spectral hardening and non-equilibrium effects, we inject an extra 2 eV per hydrogen atom at H reionization. We also inject 2 eV per hydrogen atom at z = 3.5, spread over a Gaussian redshift interval with σ(z) = 0.5, to account for the later reionization of He ii. Fig. 3 shows that this yields a thermal evolution of the IGM that agrees with observations."