At redshifts z>~2, most of the baryons reside in the smooth intergalactic medium which is responsible for the low column density Lyalpha forest. This photoheated gas follows a tight temperature-density relation which introduces a cut-off in the distribution of widths of the Lyalpha absorption lines (b-parameters) as a function of column density. We have measured this cut-off in a sample of nine high-resolution, high signal-to-noise ratio quasar spectra and determined the thermal evolution of the intergalactic medium in the redshift range 2.0-4.5. At a redshift z~3, the temperature at the mean density shows a peak and the gas becomes nearly isothermal. We interpret this as evidence for the reionization of Heii.