Question

graphite can't conduct heat while it have free electron.explain?

Answer 1

Graphite is a conductor of both heat and electricity due to loose electrons which are result of delocalised bonding.

Answer 2

graphite shows an exception of the allotropes of carbon because it has a free electron but do not conduct heat .graphite is a conductor of electricity due to its structure because each carbon atom is bonded to an atom of the graphite .the atoms of graphite and those of carbon is bonded together by the weak van der wall forces

graphite is a very unique allotrope of carbon it both  exist as a metal and a non metal at the same time graphite do not conduct heat like other compounds such as diamond in its non metalic nature