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 ( ${>}2.5\times 10^{13}$  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 ( ${\rm \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 ${\rm \mu} $ PL technique allows mapping very precisely the actual local temperature distribution in biased HEMT devices. For a gate length of 1.5  ${\rm \mu }$ 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.