The temperature of the low-density intergalactic medium is set by the balance between adiabatic cooling resulting from the expansion of the universe , and photo-heating by the UV-background .
We have analysed the Ly \alpha forest of eleven high-resolution quasar spectra using wavelets , and find strong evidence of a marked jump in the temperature at the mean density , T _ { 0 } , of 60 \pm 14 per cent over the redshift interval z = [ 3.5 , 3.1 ] , which we attribute to reionization of { He { \sc ii } ~ { } } .
The jump can be seen in all three of our spectra that straddle redshift 3.3 , at a significance of \geq 99 per cent .
Below z \sim 3.1 , our results are consistent with a smooth cooling down of the universe , as expected when adiabatic expansion dominates over photo-heating by a UV-background from QSOs and galaxies .
We find no evidence of thermal fluctuations on scales \geq 5000 km s ^ { -1 } larger than 50 per cent , which could be detected by our method , suggesting that the IGM follows a reasonably well-defined temperature-density relation .
We demonstrate that the mean wavelet amplitude \langle A \rangle \propto 1 / T _ { 0 } and calibrate the relation with hydrodynamical simulations .
We find T _ { 0 } \geq 1.2 \times 10 ^ { 4 } K at z \geq 3.6 .
Such high temperature suggest that { H { \sc i } ~ { } } reionization occured relatively recent .