Shape of high order correlation functions in CMB anisotropy maps

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 one to get insights into the general properties of the bispectrum and trispectrum. 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 bispectrum is found to have alternate signs for the successive acoustic peaks. Sign patterns for the trispectrum 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.