The 3D dispersion equation of an instability observed at the exit of a Hall thruster plasma is studied. The equation is solved numerically in the warm and cold ion cases. A parametric study of its slope shows that the mode has a group velocity close to the speed of sound. Thus, the electron temperature is estimated using collective light scattering measurements to be 29 eV. On the other hand, an analytical model is developed to fit the experimental dispersion relation. This model agrees well with the numerical results and allows an estimation of both the electron temperature and density. For the first time at the exit plane of a Hall thruster, the electron temperature and density are estimated by a non-disturbing method.