Thermal conductivities of diamond nanorods are estimated from molecular simulations as a function of radius, length, and degree of surface functionalization. While thermal conductivity is predicted to be lower than carbon nanotubes, their thermal properties are less influenced by surface functionalization, making them prime candidates for thermal management where heat transfer is facilitated by cross-links. A scaling relation based on phonon surface scattering is developed that reproduces the simulation results and experimental measurements on silicon nanowires.