Different forms of carbon or allotropes including graphene and diamond are among the best conductors of heat. In a recent report on Science, Yo Machida and a research team in the department of Physics and the Laboratory of Physics and Materials in Tokyo and France monitored the evolution of thermal conductivity in thin graphite. The property evolved as a function of temperature and thickness to reveal an intimate link between high conductivity, thickness and phonon (atomic vibrations observed as acoustic waves) hydrodynamics. They recorded the thermal conductivity (k) of graphite (8.5 µm thickness) to be 4300 Watts per meter-kelvin under room temperature. The value was well above that recorded for diamond and slightly higher than isotopically purified graphene.
Source:
https://phys.org/news/2020-02-phonon-hydrodynamics-ultrahigh-room-temperature-thermal.html