As the key component of deep-environment coring equipment, the coring device connecting structure, directly affects the operational stability and safety of the equipment under complex conditions of high temperature and high geostress. Taking the connecting structure of the coring device used in deep mining as the research object, a finite element analysis model was established. Strength verification analyses were carried out under different temperatures, different internal pressures, and coupled high-temperature and high-pressure conditions. The response characteristics of stress, strain, displacement, as well as the load and deformation of each thread tooth, were systematically investigated, and the influence on the sealing performance was discussed. The results show that: ① Under internal pressure alone, within the range of 30-120 MPa, the stress, strain, and displacement at the threads exhibit a clear linear relationship with increasing pressure. Beyond 120 MPa, the local maximum stress exceeds the yield strength, driving the structure into the elastoplastic stage. The stress distribution across thread teeth is characterized by being "concave in the middle and convex at the ends." ② Under thermal loading alone, structural displacement increases approximately linearly with temperature, primarily manifesting as an overall thermal expansion effect. ③ Under coupled temperature and pressure, the stress response is dominated by internal pressure, while the displacement response represents an approximate superposition of thermal and pressure effects. The research results provide important support for the safe service of coring devices under deep engineering conditions.