  The Sunyaev-Zel'dovich (SZ) effect has long been identified as one of the
most important secondary effects of the Cosmic Microwave Background (CMB). On
the one hand, it is a potentially very powerful cosmological probe providing us
with additional constraints and on the other hand it represents the major
source of secondary fluctuations at small angular scales (l > 1000). We
investigate the effects of the SZ modelling in the determination of the
cosmological parameters. We explore the consequences of the SZ power spectrum
computation by comparing three increasingly complex modelling, from a fixed
template with an amplitude factor to a calculation including the full
cosmological parameter dependency. We also examine the dependency of the
cosmological parameter estimation on the intra-cluster gas description used to
calculate the SZ spectrum. We show that methods assuming an SZ template bias
the cosmological parameters (by up to 2 sigmas on sigma_8) when the cosmology
used in the template deviates from the reference one. A joint CMB-SZ analysis
with a full cosmological dependency of the SZ spectrum does not suffer from
such biases and moreover improves the confidence intervals of sigma_8 and
Omega_{dm}h^2 (2.5 and 2 times respectively) with respect to a pure CMB
analysis. However, the latter method is quite sensitive to the intra-cluster
gas parameters and hence requires extra information on the clusters to
alleviate the induced biases.
