There is a reason why most good electrical conductors also conduct heat well. However, the relationship only holds, to a good approximation, in metals. Both electrical and thermal conduction in metals occur mainly via the free electrons. The relationship between electrical conductance and thermal conductance is known formally as the Wiedemann-Franz law.
Both types of conductivity are proportional to how many free electrons are present, how fast they typically move, and how far they travel before scattering off in a new direction.
Generally speaking though, there is no real relation between how well a material conducts heat and how well it conducts electricity unless
it's a metal. For other materials the heat conduction usually occurs mainly via high-frequency sound waves in the material, not by the electrically charged electrons. For example, the lattice structure of diamonds conducts heat very well, but the same structure also makes them generally very good electrical insulators.
-Matt J. +mbw
(published on 01/14/2012)