In this article, we report an antenna-coupled AlGaN/GaN high-electron-mobility transistor integrated on a hyper-hemispheric silicon lens for heterodyne detection in a 340 GHz band at room temperature. The responsivity, elevated shot noise, flicker noise, and dynamic source-drain resistance for homodyne and heterodyne detection are characterized and analyzed at different local terahertz (LO) power levels. With a LO power of only −3.9 dBm, the detector offers a conversion loss less than 28 dB and a noise-equivalent power (NEP) about −132 dBm/Hz. A threshold LO power about −5 dBm is identified above which the shot noise becomes the dominant noise source, and the intermediate-frequency response is strongly suppressed. The elevated noise and the saturation in responsivity are found to be closely related to the strong direct-current homodyne current and the charge modulation/accumulation by the LO signal. Possible solutions are discussed to further reduce the NEP and the conversion loss.