The zero-bias microwave detection capability of self-switching diodes (SSDs) based on AlGaN/GaN is analyzed in a wide temperature range, from 10 K to 300 K. The measured responsivity shows an anomalous enhancement at low temperature, while the detected voltage exhibits a roll-off in frequency, which can be attributed to the presence of surface and bulk traps. To gain a deep insight into this behavior, a systematic DC and AC characterization of the diodes has been carried out in the mentioned temperature range. DC results confirm the existence of traps and AC measurements allow us to identify their properties. In particular, impedance studies enable to distinguish two types of traps: at the lateral surfaces of the channel, with a wide spread of relaxation times, and in the bulk.