The combined dependence of the electronic and thermal characteristics in the AlGaN/GaN HEMTs supported in nano-elctronic devices was studied theoretically and numerically. The Schrödinger-Poisson equations coupled with Dual phase lag (DPL) thermal transfer equation was undertaken. Simultaneous impacts of the conduction band offset and polarization charge between the AlGaN/GaN heterointerface induce the production of the two-dimensional electron gas density (2DEG). The simulation results showed that the 2DEG density at the heterointerface increased with increase of Aluminum fraction. In addition, the simulation results of the thermalization process were found to be in good agreement with the literature. As a result, the maximum heat generation as well the maximum temperature at the heterointerface increased. The obtained result could to be useful in assessing thermal transfer in the AlGaN/GaN HEMTs nano-devices to improve their performance.