How Do Metals Conduct Heat?
In metals, few of the electrons are not fixed to one atom they normally move freely between atoms. This is the main reason that the metals are good conductor of heat and electricity. In other words if one side of the metal is hot and the other end of the metal is cold, then the electrons present on the hotter end have more thermal energy than the cold end. So as the electrons move freely they transfer energy from the hotter side to the cooler side.
Solids conduct by phononic lattice vibrations and free electron diffusion, but it is predominantly free electron diffusion in metals which is the faster method of heat conduction. Metals (eg. copper) are usually the best conductors of thermal energy. This is due to the way that metals are chemically bonded: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons and form a crystalline structure, greatly aiding in the transfer of thermal energy. The transfer of energy could be primarily by elastic impact as in fluids or by free electron diffusion as predominant in metals or phonon vibration as predominant in insulators. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from atom to atom.