To address the issues of significant thermal stress, fluctuating leakage rate, and absence of pressure self-sensing functionality in traditional sealing materials under temperature-fluctuating environments, this study conducted research on the design and preparation of a silicone rubber composite material with a centrifugally structured graphene aerogel attached to its surface. First, a three-dimensional centrifugally structured graphene aerogel was prepared via directional freezing combined with hydrothermal method. Subsequently, the aerogel was compounded with G830 silicone rubber using a surface attachment method, and the sample preparation was completed through curing and electrode co-curing processes. Systematic tests were carried out on the mechanical properties, mechano-electrical sensing performance, and sealing performance of the composite material. The results show that compared with pure G830 silicone rubber, the prepared graphene rubber exhibits near-zero thermal stress characteristics within a wide compressive strain range, with the relative change in thermal stress all below 5%. It presents segmented mechano-electrical response sensitivity within a certain pressure range, along with excellent cyclic stability and no significant signal drift. Within a wide temperature range and compression strain range, the relative change in leakage rate is significantly reduced, and the temperature stability is greatly improved compared with traditional fabric-reinforced rubber. The hierarchical graphene rubber composite material developed in this study integrates pressure self-sensing, near-zero thermal stress, and temperature-insensitive sealing performance, providing a new type of material solution for high-precision sealing monitoring scenarios under temperature fluctuations.