In order to enhance the sealing reliability of annular blowout preventers (ABOPs) under extreme temperature conditions during oil and gas exploration and development, a thermal mechanical coupling sealing performance prediction model based on Yeoh hyperelastic constitutive model was constructed using a conical rubber core as the research object. The model comprehensively considers physical parameters including wellhead pressure, temperature field, contact stress, rubber extrusion volume, effective sealing length, and ram displacement, exploring the variation law of stress with temperature. Through comparative validation between temperature experiments and finite element simulations, the model achieves a prediction error below 15%, demonstrating its applicability under complex thermo-mechanical coupling conditions. Furthermore, key sealing response parameters were systematically extracted and analyzed across a wide temperature range, revealing the underlying mechanisms of sealing performance evolution under extreme conditions. The results show that within the temperature range of -18 ℃ to 93 ℃, contact stress exhibits a “increase-decrease” trend with temperature rise, dropping sharply beyond 120 ℃ to a critical threshold below sealing design requirements, indicating a significant failure risk. High-temperature load simulations also identified potential failure-prone zones and propagation paths of the packing element, providing theoretical insights for failure mechanism analysis and structural optimization.