  We investigate the dependence of QSO Lyman-alpha absorption features on the
temperature of the absorbing gas and on the amplitude of the underlying dark
matter fluctuations. We use high-resolution hydrodynamic simulations in cold
dark matter dominated cosmological models. In models with a hotter
intergalactic medium (IGM), the increased temperature enhances the pressure
gradients between low and high density regions and this changes the spatial
distribution and the velocity field of the gas. Combined with more thermal
broadening, this leads to significantly wider absorption features in hotter
models. Cosmological models with little small scale power also have broader
absorption features, because fluctuations on the scale of the Jeans length are
still in the linear regime . Consequently, both the amplitude of dark matter
fluctuations on small scales and thermal smoothing affect the flux decrement
distribution in a similar way. However, the b-parameter distribution of Voigt
profile fits, obtained by deblending the absorption features into a sum of
thermally broadened lines, is largely independent of the amount of small scale
power, but does depend strongly on the IGM temperature. The same is true for
the two-point function of the flux and for the flux power spectrum on small
scales. These three flux statistics are thus sensitive probes of the
temperature of the IGM. We compare them computed for our models and obtained
from a HIRES spectrum of the quasar Q1422+231 and conclude that the IGM
temperature at z=3.25 is fairly high, T_0>= 15000K.
