  We estimate the power spectrum of SZ(Sunyaev-Zel'dovich)-effect-induced
temperature fluctuations on sub-degree scales by using the cross correlation
between the three-year WMAP maps and 2MASS galaxy distribution. We produced the
SZ effect maps by hydrodynamic simulation samples of the $\Lambda$CDM model,
and show that the SZ effect temperature fluctuations are highly non-Gaussian.
The PDF of the temperature fluctuations has a long tail. More than 70% power of
the SZ effect temperature fluctuations attributes to top $\sim 1%$ wavelet
modes (long tail events). On the other hand, the CMB temperature fluctuations
basically are Gaussian. Although the mean power of CMB temperature fluctuations
on sub-degree scales is much higher than that of SZ effect map, the SZ effect
temperature fluctuations associated with top 2MASS clusters is comparable to
the power of CMB temperature fluctuations on the same scales. Thus, from noisy
WMAP maps, one can have a proper estimation of the SZ effect power at the
positions of the top 2MASS clusters. The power spectrum given by these top
wavelet modes is useful to constrain the parameter of density fluctuations
amplitude $\sigma_8$. We find that the power spectrum of these top wavelet
modes of SZ effect on sub-degree scales basically is consistent with the
simulation maps produced with $\sigma_8=0.84$. The simulation samples of
$\sigma_8=0.74$ show, however, significant deviation from detected SZ power
spectrum. It can be ruled out with confidence level 99% if all other
cosmological parameters are the same as that given by the three-year WMAP
results.
