  We propose a new analysis of small scale CMB data by introducing the
cosmological dependency of the foreground signals, focusing first on the
thermal Sunyaev-Zel'dovich (tSZ) power spectrum, derived from the halo model.
We analyse the latest observations by the South Pole Telescope (SPT) of the
high-$\ell$ power (cross) spectra at 90, 150 and 220 GHz, as the sum of CMB and
tSZ signals, both depending on cosmological parameters, and remaining
contaminants. In order to perform faster analyses, we propose a new tSZ
modelling based on machine learning algorithms (namely Random Forest). We show
that the additional information contained in the tSZ power spectrum tightens
constraints on cosmological and tSZ scaling relation parameters. We combine for
the first time the Planck tSZ data with SPT high-$\ell$ to derive even stronger
constraints. Finally, we show how the amplitude of the remaining kSZ power
spectrum varies depending on the assumptions made on both tSZ and cosmological
parameters.
