By studying the photoluminescence from an n-GaN ungated MESFET, the hot carrier temperatures for lattice temperatures in the range 10-300K as a function of the applied electric field are extracted. A semi-analytical theoretical model (Energy Loss Rate model) is used to study the electron temperature as a function of the electric fields. The rate of increase of electron temperature with the external electric field provides a signature of non-equilibrium hot-phonon accumulation. When the chief electron energy loss mechanism is by the emission of LOoptical phonons, a clear signature of a hot-phonon effect is observed, with a hot-phonon lifetime in the 3-4 ps regime.The growth of InN by MBE and its structure, electronic and optical characterizations are presented. The growth condition of InN on GaN substrates using radio frequency molecular beam epitaxy (rf-MBE) is studied. Characterizations such as AFM, XRD, PL and TEM show that InN of good film quality has been achieved.