Graphite: Thermal and electrical conductivity I recently encounter this question: 

Compare, while providing an explanation, the thermal and electrical conductivity of graphite to that of diamond.

Provided answer:
Graphite conducts electricity(only across a layer) where as diamond does not. 

Diamond is better at transferring heat than graphite. 

Explanation:
Diamond is covalent network solid of carbon atoms which are linked to each other through sigma bonds. 

Graphite has a layered structure where each layer is bonded to the other later through vanderwall forces only. Each layer consists of hexagonal rings which have a delocalized pi electron network just above and below the plane. 

These delocalized pi electrons are the reason why graphite can conduct electricity along the planes, where as diamond cannot due to the lack of delocalized electrons. 

Diamond is a better conductor of heat because the transfer of heat takes place through adjacent atoms transferring their vibrational energy and diamond has a very close knit network of atoms where as graphite does not. 

My doubt:
In metals it is accepted that both electrical and thermal conductance is due the the free electrons present in the metal body. 

Graphite too has delocalized free electrons so according the same logic graphite should be both a good conductor of heat and electricity. 

So where am I or the answer provided going wrong? 

P. S. I'm writing from a mobile device due to the lack of access computers so there might be some errors. 

Edit:

J. D. Lee: Concise inorganic chemistry, fifth edition :


This would mean that the electrons are truley free since they can interact with other species nearby not preventing them from being bound to a system.
You are wrong to say that graphite has free electrons.  The electrons are bound to sheets of aromatic rings--delocalized but not free. In electrical conduction, the electron pairs are able to jump from bond to bond on the sheet and between sheets. It is worth noting that graphite has anisotropic conduction where between sheets conduction is lower than conduction along a sheet.

For thermal conduction, energizing an atom does not transmit the energy via free electrons like a metal would.  instead, you are limited to a predominately phonon driven heat transfer again, but now the structure is less dense and the carbons are less rigidly bonded.

Diamond as your correctly identified has a rigid structure that can easily conduct phonons but not electrons which gives good thermal, but not electrical conduction.