If you heat carbon in a vacuum, it sublimates straight to gas. If you heat it under extreme pressure in an inert gas atmosphere, then it can melt. Unfortunately creating such pressures in the lab is only possible with diamond anvil presses, which are themselves carbon and thus tend to sublimate from the heat, resulting in pressure vessel failure. Doing the experiment on the surface of a neutron star would work, but presents some other difficulties.
If you heat carbon in a vacuum, it sublimates straight to gas. If you heat it under extreme pressure in an inert gas atmosphere, then it can melt. Unfortunately creating such pressures in the lab is only possible with diamond anvil presses, which are themselves carbon and thus tend to sublimate from the heat, resulting in pressure vessel failure. Doing the experiment on the surface of a neutron star would work, but presents some other difficulties.