Graphene, a well-known two-dimensional sheet, has attracted strong interest for both fundamental studies and applications. Due to its high intrinsic thermal conductivity, graphene has many potential applications in thermal management, such as in heat spreaders and flexible heaters. In this paper, a graphene-based transparent flexible heat conductor for nanophotonic integrated devices is demonstrated. The graphene heat conductor is designed to deliver heat from a non-local traditional metal heater to nanophotonic integrated devices for realizing efficient thermal tuning. With the present graphene heat conductor, a thermally tuning silicon Mach-Zehnder interferometer and micro-disk have been realized with good performance in terms of heating efficiency and temporal response. This indicates that the present graphene-based transparent flexible heat conductor provides an efficient and beneficial heating method for thermally tuning nanophotonic integrated devices.