We cross-correlate WMAP and ROSAT diffuse X-ray background maps and look for common features in both data sets .
We use the power spectrum of the product maps and the cross-power spectrum to highlight a possible correlation .
The power spectrum of the product maps does not detect any correlation and the cross-power spectrum does not show any significant deviation from 0 .
We explore different explanations for this lack of correlation .
A universe with a low value of \sigma _ { 8 } could naturally explain the lack of correlation .
We also discuss the systematic effects which can affect this result , in particular the subtraction of some cluster signal from the ROSAT diffuse maps which could significantly suppress the correlation signal .
These systematic effects reduce considerably the significance of our constraints on the cosmological model .
When we include the systematic effects we find a weaker constrain on \sigma _ { 8 } allowing models with values as large as \sigma _ { 8 } = 1 ( for \Omega _ { m } = 0.3 ) to be consistent with the lack of correlation .
To illustrate the capabilities of the method with future high-quality data , we show how from the correlation signal it should be possible to predict the level of contamination of the SZ effect on the power spectrum of the CMB .
Within the systematic errors we find evidence that this contribution is negligible for WMAP and is expected to be small in experiments like ACBAR or CBI , but can be important for future high resolution experiments .