Rock fracture and rock instability at high temperatures are serious threats to the safe and efficient exploitation of deep geothermal resources. The electric potential (EP) can provide valuable information to monitor and forecast these issues. In this work, compression-shear failure tests were performed to monitor the EPs of granite samples after thermal treatment at 25 °C, 200 °C, 400 °C and 600 °C. The temporal response and non-extensive statistical characteristics of EPs subjected to different thermal treatments were analyzed. The precursory information of the EPs was studied by exploring the change in Tsallis entropy q and variance with the damage variable. The effect of thermal damage on the response mechanisms of EPs was studied using fracture surface scanning, thermogravimetry-infrared radiation (TG-IR) and scanning electron microscopy (SEM) tests. The results show that the thermal treatment affects the EP response by changing the mechanical properties, failure behavior and microstructure. With increasing treatment temperature, the average EP value gradually decreased. The probability density distributions (PDF) of the EPs under different treatment temperatures were consistent with a q-Gaussian distribution, and q increased with increasing treatment temperature. According to the critical theory, the damage state of samples is reflected by the evolution of q and variance based on the EPs and can provide precursory information for instability failure. With increasing treatment temperature, the initial thermal damage becomes more severe, the fractal dimension and roughness of the fracture surface increase, and the unstable propagation of microcracks and precursory points appears earlier.