  We apply the hierarchical clustering model and non-linear perturbation theory
to the cosmological density and temperature fields. This allows us to calculate
the intergalactic gas pressure power spectrum, SZ anisotropy power spectrum,
skewness and related statistics. Then we show the effect of the
non-gravitational heating. Our model confirms recent simulations yielding mass
weighted gas temperature \bar{T}_g \sim 0.35 keV and reproduces the power
spectra found in these simulations.
  While the SZ effect contains only angular information, we show that it is
possible to extract the full time resolved gas pressure power spectrum when
combined with galaxy photometric redshift surveys by using a variation on the
cross-correlation. This method further allows the disentanglement of the
gravitational and the non-gravitational heating.
