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We investigate the thermal history of the intergalactic medium (IGM) in the redshift interval z=1.7--3.2 by studying the small-scale fluctuations in the Lyman alpha forest transmitted flux. We apply a wavelet filtering technique to eighteen high resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph (UVES), and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied. From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent, independent wavelet-based measurements. We also perform a reanalysis of the same data set using the Lyman alpha forest flux probability distribution function (PDF), which has previously been used to measure the IGM temperature-density relation. This provides an important consistency test for measurements of the IGM thermal state, as it enables a direct comparison of the constraints obtained using these two different methodologies. We find the constraints obtained from wavelets and the flux PDF are formally consistent with each other, although in agreement with previous studies, the flux PDF constraints favour an isothermal or inverted IGM temperature-density relation. We also perform a joint analysis by combining our wavelet and flux PDF measurements, constraining the IGM thermal state at z=2.1 to have a temperature at mean density of T0/[10^3 K]=17.3 +/- 1.9 and a power-law temperature-density relation exponent gamma=1.1 +/- 0.1 (1 sigma). Our results are consistent with previous observations that indicate there may be additional sources of heating in the IGM at z

We present a measurement of the Lyman α flux probability distribution function (PDF) obtained from a set of eight high-resolution quasar spectra with emission redshifts in the range 3.3 ≤z≤ 3.8. We carefully study the effect of metal absorption lines on the shape of the PDF. Metals have a larger impact on the PDF measurements at lower redshift, where there are relatively fewer Lyman α absorption lines. This may be explained by an increase in the number of metal lines that are blended with Lyman α absorption lines towards higher redshift, but may also be due to the presence of fewer metals in the intergalactic medium (IGM) at earlier times. We also provide a new measurement of the redshift evolution of the effective optical depth, τeff, at 2.8 ≤z≤ 3.6, and find no evidence for a deviation from a power-law evolution in the log (τeff)–log (1 +z) plane. The flux PDF measurements are furthermore of interest for studies of the thermal state of the IGM at z≃ 3. By comparing the PDF to state-of-the-art cosmological hydrodynamical simulations, we place constraints on the temperature of the IGM and compare our results with previous measurements of the PDF at lower redshift. At redshift z= 3, our new PDF measurements are consistent with an isothermal temperature–density relation, T=T0Δγ− 1, with a temperature at the mean density of T0= 19 250 ± 4800 K and a slope γ= 0.90 ± 0.21 (1σ uncertainties). In comparison, joint constraints with existing lower redshift PDF measurements at z < 3 favour an inverted temperature–density relation with T0= 17 900 ± 3500 K and γ= 0.70 ± 0.12, in broad agreement with previous analyses.