Heat conduction depends on the electronic configuration, density, temperature and dimensions of the material. Conduction should not be confused with conductivity, which is dimension independent.
Heat conduction involves the direct transfer of heat through matter by means of physical contact. Conduction involves the flow of internal energy from a higher temperature region to a lower temperature one. Material conductivity depends on the number of free carrier particles that can transfer kinetic energy from one part of the material to another. As the number of carriers increases, the conductivity does as well.
Ionic solids have low conductivities because their ions are fixed in crystal lattice positions with their electrons bound to these positions. Metallic solids have high conductivities because their valence-shell electrons, which act as free carriers, are delocalized. This means that they are free to move through the structure, transferring kinetic energy through this motion. The best elemental metal conductors, in order of decreasing conductivity at room temperature are silver, copper, gold, aluminum and tungsten. The best conductor of all is liquid helium, which can only exist at temperatures right above absolute zero.
Absolute temperature negatively affects the conductivity of metallic materials, because as temperature increases, the metal ion cores start vibrating more vigorously around their equilibrium positions. This increases the likelihood of an electron being hindered or deflected by these metal cores, decreasing conductivity.