This paper reports on the transport and material characterization of AlGaN/GaN heterostructures. We compared the overheating temperatures in the transmission line model patterned devices during normal operation and analyze their dependence on the buffer thickness in order to optimize the thermal budget of the structures. It is demonstrated that noise spectra can be used to monitor the transport mechanisms and determine the activation energy of the traps. Small-dose gamma irradiation is used as an effective treatment for improving the structural properties. Based on cathodoluminescence and X-ray diffraction spectra shape, we explain the improvement as a result of the relaxation of elastic strains and structural-impurity ordering in the AlGaN barrier layer under irradiation. An irreversible improvement in mobility of the electrons in the channel, controlled by a proper dose of gamma radiation treatment, at considerably reduced self-heating is promising to achieve novel quantum transport regimes on the nanoscale.