Understanding the impact of irradiation and temperature on the mechanical properties of GaN single crystals holds significant relevance for rational designs and applications of GaN-based transistors, lasers, and sensors. This study systematically investigates the influence of C-ion irradiation and temperature on pop-in events, hardness, Young's modulus, and fracture behavior of GaN single crystals through nanoindentation experiments. In comparison with unirradiated GaN samples, the pop-in phenomenon for ion-irradiated GaN samples is associated with a larger critical indentation load, which decreases with increasing temperature. Both unirradiated and ion-irradiated GaN samples exhibit a decline in hardness with increasing indentation depth, while Young's moduli do not exhibit a clear size effect. In addition, intrinsic hardness displays an inverse relationship with temperature, and ion-irradiated GaN single crystals exhibit greater intrinsic hardness than their unirradiated counterparts. Our analysis further underscores the significance of Peierls stress during indentation, with this stress decreasing as temperature rises. Examinations of optical micrographs of indentation-induced fractures demonstrate an irradiation embrittlement effect. This work provides valuable insights into the mechanical behavior of GaN single crystals under varying irradiation and temperature conditions.