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 .