According to the photo-heating model of the intergalactic medium ( IGM ) , He II reionization is expected to affect its thermal evolution . Evidence for additional energy injection into the IGM has been found at 3 \lesssim z \lesssim 4 , though the evidence for the subsequent fall-off below z \sim 2.8 is weaker and depends on the slope of the temperature–density relation , \gamma . Here we present , for the first time , an extension of the IGM temperature measurements down to the atmospheric cut-off of the H I Lyman- \alpha forest at z \simeq 1.5 . Applying the curvature method on a sample of 60 UVES spectra we investigated the thermal history of the IGM at z < 3 with precision comparable to the higher redshift results . We find that the temperature of the cosmic gas traced by the Ly- \alpha forest [ T ( \bar { \Delta } ) ] increases for increasing overdensity from T ( \bar { \Delta } ) \sim 22670 K to 33740 K in the redshift range z \sim 2.8 - 1.6 . Under the assumption of two reasonable values for \gamma , the temperature at the mean density ( T _ { 0 } ) shows a tendency to flatten at z \lesssim 2.8 . In the case of \gamma \sim 1.5 , our results are consistent with previous ones which indicate a falling T _ { 0 } for redshifts z \lesssim 2.8 . Finally , our T ( \bar { \Delta } ) values show reasonable agreement with moderate blazar heating models .