[redleader]

Heat flow through most close packed solids, ie metals, is by phonons, lattice vibrations, which travel through the material. these vibrations are going to be largely affected by the bond strength/length between atoms.

Metals are not diamonds. Conduction in metals is due to electrons passing between atoms through the conduction band. Phonons are in strongly bonded covalent crystals like diamond. That is why thermal and electrical conductivity are so closely related in metals, but not in diamond.

Allow me to quote my text book:

However, it is a common observation that the conductivity of a metal decreases as the temperature increases. The mobility in a metal is limited by electron scattering. This is dominated by impurities and crystal defects at low temperatures, but is caused mainly by lattice vibrations (phonons) above room temperature. Since thermal vibrations increase with temperature, the electronic mobility and, hence, overall conductivity decreases as the temperature increases in a metal. Conductivity in a metal is also very sensitive to impurities and other defects which scatter the electrons. The non-directional metallic bond allows defects to be accommodated with relative small increases in energy.

and again from another chapter:

Metals also have very high thermal conductivity, but this is due to the heat carried by the electron gas.