Higher candidates only Metals conduct heat better than any other material. This is because of their structure. Metals have metallic bonds, which generate a giant structure. This giant structure enables the outer electrons to move freely. It is these electrons which conduct the heat energy.
Conduction occurs when the electrons are excited by heat energy and start to move faster.
They move through the metal by diffusion carrying the heat energy with them. They also collide with other electrons and pass on some heat energy this way.