Reliable measurements of electron properties are key for the validation of simulations of Hall thrusters and similar plasma sources. In this paper, a recently-developed incoherent Thomson scattering diagnostic is successfully applied to electron property measurement in a low-power Hall thruster discharge. Investigations on both conventional and magnetically-shielded architectures of electron properties along radial and azimuthal directions are performed. The high diagnostic sensitivity gives access to electron property measurements in a plasma environment with densities as low as 10^{16} m^{−3}. Electron temperatures reaching several tens of eV and drift velocities on the order of 10{6} m s^{−1} are measured in the exit plane region. Axial distance and discharge voltages explorations were realized. Thomson spectrum distributions characteristic of electrons out of thermal equilibrium were observed at low discharge voltage and close from the exit plane, the derived EEDF suggests the presence of a second electron population around 100 eV.