Which substance has the highest thermal conductivity

Q. Carbon has highest thermal conductivity of any known substance. Then why carbon rotted tools don't overheat and are extensively used for striking and cutting proposes? Is it that the good thermal conductors don't overheat? Please explain.

Q. Which among the following metals have the highest thermal conductivity?

Q. Which of the following has highest conductivity?

Q. Which of the following which has the highest molar conductivity?

Q. Which of the following has the highest molar conductivity?