We report a new experimental technique to study the form of the hot electron distribution function in GaAs/AlGaAs heterostructures. A weak periodic surface potential induces Smith-Purcell-FIR-radiation of the electric field driven hot electrons in the 2-dimensional electron gas directly reflecting their velocity distribution. The FIR- radiation is detected by a magnetic field tuned InSb-detector. In samples with very low electron concentration and high mobility the emission spectra show a significant shift to higher energies and develop a steep high energy slope with increasing electric field when we use the geometry with grating vector (\mathrm{q}) directed parallel to the electric field ( (\mathrm{q} \mathrm{E}) ). In the geometry (\mathrm{q} \perp \mathrm{E}) smooth decays are observed at lower energies. Comparison of the results with theory gives experimental evidence of a non-equilibrium shape of the distribution caused by the onset of LO-Phonon emission. In addition, the hot electron mean free path of the heated distribution is derived by investigating the experimental emission spectra as a function of the grating period length. The influence of a limited hot electron mean free path on the spectral width is described in terms of a Fourieranalysis of the interaction potential. In drift direction a mean free path of (\lambda=200 \mathrm{~nm}) is obtained, whereas the mean free path is smaller in the direction perpendicular to the drift direction.