In this paper, we study the two-dimensional electron heating effects in an lectric field in a quantum well at a GaN/AlGaN heterointerface. The energy loss rates of two-dimensional electrons due to interaction with interface and half-space optical phonons were calculated. The calculations took into account the dynamical screening of polarization potential by free electrons and the hot-phonon effect. The energies of three interface phonon modes were calculated.  Calculation of the energy loss rate related to the interface phonon scattering showed that at electron temperatures above 70 K, the main contribution to scattering is made by the high energy mode of 96.2 meV. If the electron  temperature exceeds 40 K, then the contribution of half-space phonons to energy losses exceeds the contribution of interface phonons. The field dependence of the electron temperature was calculated taking into account various  effects, affecting the charge carrier heating. The calculated electron temperature reaches its highest values with simultaneous consideration of dynamical screening and the hot-phonon effect. The spectra of radiation emitted by hot two-dimensional electrons were calculated for several electron temperatures.