  We present a phenomenological investigation of non-Gaussian effects that
could be seen on CMB temperature maps. Explicit expressions for the temperature
correlation functions are given for different types of primordial mode
couplings. We argue that a simplified description of the radial transfer
function for the temperature anisotropies allows to get insights into the
general properties of the bi and tri-spectra. The accuracy of these results is
explored together with the use of the small scale approximation to get explicit
expressions of high order spectra. The bi-spectrum is found to have alternate
signs for the successive acoustic peaks. Sign patterns for the trispectra are
more complicated and depend specifically on the type of metric couplings. Local
primordial couplings are found to give patterns that are different from those
expected from weak lensing effects.
