Embodiments of the present invention provide structures and methods for heat suppression in finFET devices. Fins are formed in a semiconductor substrate. A graphene layer is formed on a lower portion of the sidewalls of the fins. A shallow trench isolation region is disposed on the structure and covers the graphene layer, while an upper portion of the fins protrudes from the shallow trench isolation region. The graphene layer may also be deposited on a top surface of the base semiconductor substrate. The graphene serves to conduct heat away from the fins more effectively than other dielectric materials.