It is observed experimentally that high electron mobility transistor devices with short channel length processed from nitride AlInN/AlN/GaN heterostructures containing 2D electron gases (2DEGs) with densities beyond 2 x 10(13) cm(-2) exhibit temperatures up to 1000 K if they are driven at high drain-source voltages. Corresponding current-voltage (IV) characteristics show a peaklike behavior with a maximum saturation current (I-DS,I-max) up to 2 A/mm. The goal of this article is to describe device heating in the framework of LO phonon statistics and its dependence on channel length, carrier density, and applied voltage. The strong channel heating, on the other hand, affects the transport mobility and must be taken into account to correctly interpret IV characteristics and resolve the discrepancy with metal oxide semiconductor field effect transistor models. Furthermore, the breakdown of ohmic contacts can directly be related to the channel temperature, i.e., the channel reaches the melting point of the contact metallization. In addition, the model correctly predicts the behavior of IV curves versus 2DEG density and transistor initial ambient temperature. For 2DEGs confined in triangular potential wells formed at the heterointerface, a maximum IDS is found for 2DEG densities between 2 x 10(13) and 3 x 10(13) cm(-2). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3552932]