We characterise the thermal state of the intergalactic medium (IGM) in ten redshift bins in the redshift range $2 leq z leq 4$ with a sample of 103 high resolution, high S/N Ly$alpha$ forest spectra using four different flux distribution statistics. Our measurements are calibrated with mock spectra from a large suite of hydrodynamical simulations post-processed with our thermal IGM evolution code CITE, finely sampling amplitude and slope of the expected temperature-density relation. The thermal parameters inferred from our measurements of the flux power spectrum, Doppler parameter distribution, as well as wavelet and curvature statistics agree well within their respective errors and all clearly show the peak in temperature and minimum in slope of the temperature density relation expected from HeII reionization. Combining our measurements from the different flux statistics gives $T_0=(14750 pm 1322)$K for the peak temperature at mean density and a corresponding minimum slope $gamma = 1.225 pm 0.120$. The peak in the temperature evolution occurs at $z approx 3$, in agreement with previous measurements that had suggested the presence of such a peak, albeit with a large scatter. Using CITE, we also calculate the thermal state of the IGM predicted by five widely used (spatially homogeneous) UV-background models. The rather rapid thermal evolution inferred by our measurements is well reproduced by two of the models, if we assume (physically well motivated) non-equilibrium evolution with photo-heating rates that are reduced by a moderate factor of $sim 0.7-0.8$. The other three models predict HeII reionization to be more extended with a somewhat earlier as well as higher temperature peak than our measurements suggest.
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