Quasi-two-dimensional electron gas (2DEG) transport properties in a selectively doped GaAs/AlxGa1-xAs (x=0.2 and 0.3) heterostructures, especially in warm and hot electron conditions, are discussed. To get insights into distinct characteristics of 2DEG, heated electron temperature and cooling process under applied electric fields were studied through analyses of quantum oscillations in magnetoresistance. The application of pulsed Hall measurements to GaAs/AlGaAs heterostructures have demonstrated a significant electric field dependence of Hall mobility. This distinct field dependence of 2DEG mobility indicated the change of scattering process from screened ionized impurity scattering and electron-electron scattering (in low fields) to the electron-phonon interactions (in high fields). We observed 2DEG velocity as high as 2.9 ×107 cm/sec at 4.2 K. The screening effect of polar coupling between hot electrons and LO phonons is discussed.