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The temperature gradient and mismatching between the thermal expansion of the core and flange readily lead to cracks and discharges on the core surface of the dry-type valve-side bushing, which severely impact the safety of power systems. It is vital to clarify the cracking risk of bushing cores under temperature gradients and establish corresponding control methods. The mechanical properties of epoxy resin impregnated paper (ERIP) material were measured in this study at different temperatures, and a thermal–mechanical coupling simulation model was established. The thermal and stress distributions of the core were obtained and the cracking risk was defined accordingly. The crack development mode was explored as it relates to the phase-field mode. Various elastic cushion materials affecting the stress distribution of the core were investigated. The results show that the mechanical properties of the ERIP material decrease rapidly as the temperature increases. When under severe working conditions, the maximum first principal stress of the core may be significantly higher than the tensile strength of the ERIP material resulting in significant axial cracks. Adding an elastic cushion layer made of polyurethane rubber can effectively relax the interface stress and reduce the cracking risk. [ABSTRACT FROM AUTHOR]