When writing with a pencil, there seems to be quite a lot of friction - which seems like it would induce heat.
How hot would the tip of a #2 pencil get writing on normal copy paper?
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Graphite (pencil "lead") is an allotrope of carbon that occurs in layers of carbons arranged into hexagons, tessellating the plane. Each carbon is $sp^2$ bonded and each layer is one atom thick. The bonds holding the carbons in one plane together are incredibly strong, uniform covalent bonds of strength ~1.33, and the carbons are in a very stable hexagonal arrangement. These bonds are incredibly difficult to break, hence graphite's extraordinarily high melting point (several thousand kelvins).
By contrast, there are only weak dispersion forces holding different planes together, which are easily broken. When you write, you are breaking these bonds to leave graphite layers on the paper.
Imagine a deck of cards. Even if you're the fastest dealer in the world, the deck never heats up. Why? Because however much friction is felt at the interface between the top card and the one under it, it is only felt for a moment and then new, cool cards feel it.
Because the paper is removing the graphite from the pencil through friction, the heat is not transfered to the tip because the matetrial that would have been heated by the friction between the paper and the tip has been left on the piece of paper. So, to heat the penicil tip up, my thoughts would be that you would have to write with the pencil quicker then it is possible or for very extened amounts of time and even then because of the part that may have been heated by friction, it is then removed. This leads that the tip of a pencil does not even get hot during writing.