Geothermal energy is increasingly recognized as a potential of replenishing fossil fuels and meeting decarbonization obligations. HP/HT drilling is also increasingly recognized as a tool to provide an adequate supply of oil/gas. In these two types of activity, the high temperature is the common challenge for drilling. Under high temperature, rocks usually behave differently compared to the ambient condition. Whether the popular failure criteria can be used to evaluate wellbore stability under geothermal conditions is a question which has not been answered yet. In this paper, the triaxial compression tests under different temperature for six types of rock (Strathbogie granite, Tak granite, Tournemire shale, Slate, Carthage marble, and Crab Orchard sandstone) have been used to evaluate six different failure criteria. Two methods have been implemented to obtain rock cohesion and internal friction angle, which are grid search algorithm and Mohr failure line method. Both methods show that Modified Lade is the failure criterion that provides the best performance in predicting rock failure under geothermal drilling. The grid search algorithm guarantees the best performance of the failure criteria, providing with the best-fit rock parameters. The more practical method of Mohr failure line can still generate engineering reasonable predictions if a safety factor of 1.1 is considered, but only the Modified Lade should be used. The thermal influence on rock parameters is also analyzed and the cohesion is found to be decreased with the improvement of temperature, whereas the internal friction angle does not have a consistent relationship with temperature. Overall, considering the considerable variance of depth (several kilometers) and temperature (several hundred degree Celsius) of geothermal and deep oil/gas resources, the Modified Lade has proven to be the best choice to perform wellbore stability analysis.