  Non-linear evolution of cosmological energy density fluctuations triggers
deviations from Gaussianity in the temperature distribution of the cosmic
microwave background. A method to estimate these deviations is proposed. N-body
simulations -- in a $\Lambda$CDM cosmology -- are used to simulate the strongly
non-linear evolution of cosmological structures. It is proved that these
simulations can be combined with the potential approximation to calculate the
statistical moments of the CMB anisotropies produced by non-linear gravity.
Some of these moments are computed and the resulting values are different from
those corresponding to Gaussianity.
