What makes a metal a good conductor of heat

Metals conduct heat well for two reasons: metal ions pack very closely together in their molecular lattice, and electrons drifting through the metal carry kinetic energy around the lattice. The result is a quick elevation in particle motion that is expressed through heat energy. This conductivity is one reason why one rarely sees metal playground equipment anymore - although the slides go a lot faster than plastic ones, sitting on a slide on a hot summer afternoon is often quite painful

Metals are good conductors of heat for two reasons:

the close packing of the metal ions in the lattice. the delocalised electrons can carry kinetic energy through the lattice.