Conduction transfers energy from hot to cold regions of a substance by molecular interaction. In fluids, the exchange of energy is primarily by direct impact. In solids, the primary mechanism is relative lattice vibrations, enhanced in the case of metals by drift of free electrons through the lattice. Thus, good electrical conductors are also good heat conductors. Both the molecular and the free-electron interactions are well founded in theoretical atomic physics.
[from White, Frank M., Heat Transfer]