We propose a microwave diode based on a modulation-doped GaAs/Al(0.25)Ga(0.75)As structure. The principle of the diode operation relies on a non-uniform heating of the two-dimensional electron gas in microwave electric fields arising due to the asymmetric shape of the device. The voltage sensitivity of the diode at room temperature is dose to 0.3 V W(exp -1) at 10 GHz, which is comparable to the value obtained using similarly shaped and sized diodes based on bulk n-GaAs. At liquid nitrogen temperature, the voltage sensitivity strongly increases reaching a value of 20 V W(exp -1) due to the high mobility of the two-dimensional electron gas. The detected signal depends linearly on power over 20 dB, until hot-electron real-space-transfer effects begin to predominate. We discuss noise temperature measurements at 10 GHz, consider the frequency dependence of the voltage sensitivity in the microwave range and compare the performance data of the proposed device and the asymmetrically shaped bulk GaAs diode within the 10 GHz-2.5 THz frequency range.