The temperature of the diffuse, photoheated intergalactic medium (IGM) depends on its reionization history because the thermal timescales are long. The widths of the hydrogen Lyα absorption lines seen in the spectra of distant quasars that arise in the IGM can be used to determine its temperature. We use a wavelet analysis of the Lyα forest region of quasar spectra to demonstrate that there is a relatively sudden increase in the line widths between redshifts z ≈ 3.5 and 3.0, which we associate with entropy injection resulting from the reionization of He II. The subsequent falloff in temperature after z ≈ 3.5 is consistent with a thermal evolution dominated by adiabatic expansion. If, as expected, the temperature also drops rapidly after hydrogen reionization, then the high temperatures inferred from the line widths before He II reionization imply that hydrogen reionization occurred below redshift z = 9.