  We use the probability distribution function (PDF) of the lya forest flux at
z=2-3, measured from high-resolution UVES/VLT data, and hydrodynamical
simulations to obtain constraints on cosmological parameters and the thermal
state of the intergalactic medium (IGM) at z 2-3. The observed flux PDF at z=3
alone results in constraints on cosmological parameters in good agreement with
those obtained from the WMAP data, albeit with about a factor two larger
errors. The observed flux PDF is best fit with simulations with a matter
fluctuation amplitude of sigma_8=0.8-0.85 \pm 0.07 and an inverted IGM
temperature-density relation (gamma ~ 0.5-0.75), consistent with our previous
results obtained using a simpler analysis. These results appear to be robust to
uncertainties in the quasar (QSO) continuum placement. We further discuss
constraints obtained by a combined analysis of the high-resolution flux PDF and
the power spectrum measured from the Sloan Digital Sky Survey (SDSS) lya forest
data. The joint analysis confirms the suggestion of an inverted
temperature-density relation, but prefers somewhat higher values (sigma_8 ~
0.9) of the matter fluctuation amplitude than the WMAP data and the best fit to
the flux PDF alone. The joint analysis of the flux PDF and power spectrum (as
well as an analysis of the power spectrum data alone) prefers rather large
values for the temperature of the IGM, perhaps suggesting that we have
identified a not yet accounted for systematic error in the SDSS flux power
spectrum data or that the standard model describing the thermal state of the
IGM at z ~ 2-3 is incomplete.
