Abstract Heat and stress transfer at an interface are crucial for the contact‐based tactile sensing to measure the temperature, morphology, and modulus. However, fabricating a smart sensing material that combines high thermal conductivity, elasticity, and good adhesion is challenging. In this study, a composite is fabricated using a directional template of vertically aligned folded graphene (VAFG) and a copolymer matrix of poly‐2‐[[(butylamino)carbonyl]oxy]ethyl ester and polydimethylsiloxane, vinyl‐end‐terminated polydimethylsiloxane (poly(PBA x ‐ ran ‐PDMS)). With optimized chemical cross‐linking and supermolecular interactions, the poly(PBA‐ ran ‐PDMS)/VAFG exhibits high thermal conductivity (15.49 W m −1 K −1 ), an high elastic deformation, and an interfacial adhesion of up to 6500 N m −1 . Poly(PBA‐ ran ‐PDMS)/VAFG is highly sensitive to temperature and pressure and demonstrates a self‐learning capacity for manipulator applications. The smart manipulator can distinguish and selectively capture unknown materials in the dark. Thermally conductive, elastic, and adhesive poly(PBA‐ ran ‐PDMS)/VAFG can be developed into core materials in intelligent soft robots.