We have known for a long time that graphene has in-plane thermal conductivity ranging between 2000 and 4000 $W m^{-1} K^{-1}$. But in order to model heat transport on a sheet of graphene, we need more than the conductivity: we also need specific heat in order to obtain the thermal diffusivity that is used in the equation.
I couldn't find any measurement results online for this quantity. I've only seen some crude estimates based on phonon transport, but even so, no specific figures.
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