Crack-free lattice-matched Al0.85In0.15N/GaN heterostructures were grown on sapphire substrates with barrier thicknesses up to 100 nm which exhibit very high polarization-induced electron sheet density (>2.5 x 10(13) cm(-2)) located at the heterointerface. These layers have been further processed as high electron mobility transistors (HEMTs). Optical characterization of these structures was carried out by photoluminescence and microphotoluminescence (mu PL) for different biased voltages. The insertion of an InGaN back-barrier unambiguously reveals that spatially direct optical recombinations occur within the AlInN alloy. Since the GaN excitonic bandgap is very sensitive to local temperature changes, the mu PL technique allows mapping very precisely the actual local temperature distribution in biased HEMT devices. For a gate length of 1.5 mu m temperatures up to 1130 K were found at a drain-source voltage of 20 V thus indicating the presence of a hot phonon bath.