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[Display omitted] Both high through-plane thermal conductivity and low elastic modulus can reduce thermal interface resistance, which is important for thermal interface materials. The internal porous structure of graphene aerogel (GA) makes it to have a low elastic modulus, which results in its good compressibility. Also, the network structure of GA provides thermal conducting paths, which improve the through-plane thermal conductivity of GA. Annealing GA at 3000 °C helps to remove oxygen-containing functional groups and reduces defects. This greatly improves its crystallinity, which further leads to the improvement of its through-plane thermal conductivity and it has a low modulus of 1.37Mpa. The through-plane thermal conductivity of GA annealed at 3000 °C (GA-3000) was improved as the pressure increased and got to 2.93 W/ m K at a pressure of 1.13 MPa, which is 30 times higher than other graphene-based thermal interface materials (TIMs). These discoveries offer a novel approach for preparing excellent TIMs. [ABSTRACT FROM AUTHOR]