  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<4.
