The adequate interfacial pressure of silicone rubber in cable intermediate joints is a basic condition to ensure the normal operation of cable joints, while high temperature and ageing in the operation of actual cables and accessories would affect the magnitude of interfacial pressure. The uniaxial tensile force of two different silicone rubbers for 10 kV cold-shrink joints at different temperatures and thermal ageing times was measured by experiment, and the Yeoh rubber intrinsic structure model was fitted according to the measured data. The material model was embedded into a two-dimensional axisymmetric finite element simulation model of the structure, and the relationship between the interference, temperature, thermal ageing time and interfacial pressure was investigated. The results show that the interfacial pressure increases linearly with the increase in interference. At the same interference, the interfacial pressure at the root of insulating silicone rubber and semiconducting silicone rubber increased by 9.1%, 12.3%, 6.4% and 9.2%, 16.3%, 5.6%, respectively, at 50, 75, and 100 °C compared with room temperature, and the largest interfacial pressure of cable joints was at 75 °C. Using the established ageing life prediction model based on the Arrhenius principle, the service life of the accessories was predicted to be 28.9 years at 90 °C of operating temperature and interfacial pressure greater than 55% of initial interfacial pressure.