Keep in mind graphite conducts thermally in a very different manner than metals do.
It is generally accepted that graphite is a phonon conductor and that >99% of heat is transported by phonons or quantized lattice vibrations. The thermal conductivity in layer planes in more than 200 times the conductivity out of plane. This makes graphite a very good conductor in two directions "a" and "b" and virtually an insulator in the third direction"c". The thermal conductivity of any graphite assembly is critically dependent on the orientation of the layer planes.
Here is a more detailed explanation comparing diamond to graphite:
" Diamond is one of the best thermal conductors known, in fact diamond is a better thermal conductor than many metals (thermal conductivity (W/m-K): aluminum=237, copper=401, diamond=895). The carbon atoms in diamond are sp3 hybridized and every carbon is bonded to 4 other carbon atoms located at the vertices of a tetrahedron. Hence the bonding in diamond is a uniform, continuous 3-dimensional network of C−C single (sigma) bonds. Graphite on the other hand is formed from sp2 hybridized carbon atoms that form a continuous 2-dimensional sigma and pi bonding network. This 2-dimensional network forms sheets of graphite, but there is little connection between the sheets, in fact, the sheet-sheet separation is a whopping ~3.4 angstroms. This might lead us to suspect that heat conduction in the 2-dimensional sheet of graphite would be superior to diamond, but that heat conduction between graphite sheets would be very low. This is, in fact, an accurate description of thermal conduction in graphite. Thermal conductivity parallel to the graphite sheets=1950, but thermal conduction perpendicular to the sheet = 5.7. Therefore, when we consider thermal conduction over all possible directions (anisotropic) diamond would be superior to graphite.
I'd just like to touch on the mechanisms behind thermal conductivity.
There are two ways in which heat is transmitted through solids: phonons and electronic conductivity. The latter occurs in electrically conductive solids, where conduction band electrons are free to move throughout the structure, carrying thermal energy along with them. This is a significant component to the thermal conductivity of metals and explains some of the in-plane conductivity of graphite. Electrically conductive solids tend to also be good thermal conductors for this reason, but this mode of conduction is not accessible to diamond.
Phonons and electrons travel very well along graphite's graphene sheets, but poorly between them, due to weak inter-layer interactions and the large distance between layers, explaining the anisotropy of its thermal and electronic conductivity.
Metals exhibit both modes of thermal conduction in varying degrees of importance and conduct isotropically since they lack the layered structure of graphite."
From:
https://chemistry.stackexchange.com/questions/12404/why-does-diamond-conduct-heat-better-than-graphite
