In order to investigate possibilities to measure non-Gaussian signatures of the non-linear iSW effect , we study in this work the family of mixed bispectra \langle \tau ^ { q } \gamma ^ { 3 - q } \rangle and trispectra \langle \tau ^ { q } \gamma ^ { 4 - q } \rangle between the integrated Sachs-Wolfe ( iSW ) temperature perturbation \tau and the galaxy over-density \gamma .
We use standard Eulerian perturbation theory restricted to tree level expansion for predicting the cosmic matter field .
As expected , the spectra are found to decrease in amplitude with increasing q .
The transition scale between linear domination and the scales , on which non-linearities take over , moves to larger scales with increasing number of included iSW source fields q .
We derive the cumulative signal-to-noise ratios for a combination of Planck CMB data and the galaxy sample of a Euclid -like survey .
Including scales down to \ell _ { \mathrm { max } } = 1000 we find sobering values of \sigma \simeq 0.83 for the mixed bispectrum and \sigma \simeq 0.19 in case of the trispectrum for q = 1 .
For higher values of q the polyspectra \langle \tau ^ { 2 } \gamma \rangle and \langle \tau ^ { 3 } \gamma \rangle are found to be far below the detection limit .