This study focuses on the semiconductive silicone rubber of 10 kV cold-shrink accessories. Accelerated thermal aging tests were conducted on the semiconductive silicone rubber, obtaining tensile stress–strain curves at various time points after thermal aging. The corresponding parameters of the Yeoh hyperelastic model were calculated. The results indicate that the initial shear modulus of the samples decreases with the increase in the aging temperature and time. Microscopic morphology, changes in cross-sectional content, thermal residual values, and chemical structure changes of the samples after aging were studied using electron microscopy, EDS testing, TG curves, and Fourier spectra. The results show that the surface roughness of the aged semiconductive silicon rubber increases, the residual values decrease, the thermal stability decreases, the main chain absorbance decreases, the main chain integrity decreases, and the organic functional groups Si-CH3 and Si(CH3)2 decrease, leading to a reduction in organic content.