We have investigated the radiative decay of hot two-dimensional (2D) plasmons in Al0.3Ga0.7As/ GaAs heterostructures by far-infrared emission spectroscopy and determined the spectral line shape of the radiation. Narrowband plasmon emission lines are obtained in the terahertz regime. The experimentally observed energies of plasmon emission are in good agreement with the results of a recently developed full grating theory. The plasmon emission intensity is found to increase with increasing input electrical power to the electron system and follows the Bose–Einstein distribution law characterized by the electron temperature of the hot 2D electron system. This fact indicates that 2D plasmons are thermally excited in the present experimental regime.