Friday physics fun: most electrical insulators do not conduct heat well, but diamonds are impressively good thermal conductors. Why? 
Heat is random vibrations of atoms and molecules. When you heat something you are shaking it up on the molecular level. In the microwave EM fields shake water molecules; in the toaster a current of electrons hits flaws in a metal wire, shaking up the metal lattice.
On the micro scale it makes sense to treat these vibrations as particles, phonons. They can collide, scatter from atoms, and are quantized just like real particles. Thermal conduction is a flow of random phonons. news.mit.edu/2010/explained…
In a metal there is an "electron gas": the outer electrons of atoms move around freely. This is why they conduct electricity well, reflect light and even emit electrons when heated enough. en.wikipedia.org/wiki/Free_elec…
When you heat a metal it becomes less electrically conductive. The electrons bump into the phonons and cannot flow as freely. en.wikipedia.org/wiki/Wiedemann…
Phonons have the same problem with defects in non-metal crystal lattice (and even more trouble in glass). Since diamonds tend to have very neat lattices with strong bonds it is easy for phonons to flow: good thermal conductivity. Despite being electrical insulators.
Phonons scatter each other, so thermal conductivity of diamond increases as it is cooled. However, there is a limit: below -150C (x5 room temp conductivity) there are fewer available phonon modes and it becomes harder to transport heat again. diamond-materials.com/EN/cvd_diamond…
Normal diamonds are 1.1% C13 instead of C12. The heavier atoms scatter phonons a bit: remove them, and conduction works better. One very cool effect of this is that one can increase diamond thermal conductivity by 50% or more by making it from pure C12. journals.aps.org/prb/abstract/1…
Some phonons in diamond have energy way beyond the pedestrian thermal phonons and do not interact with them. That allows quantum entangling them using laser pulses, making room-temperature quantum systems.
www2.physics.ox.ac.uk/research/ultra…
www2.physics.ox.ac.uk/research/ultra…
The idea that good electrical conductors are good thermal conductors misled sf author Larry Niven in his novel "Ringworld" to think superconductors should be heat superconductors (a mistake others repeated). In fact, they are really bad heat conductors. arxiv.org/abs/0904.0388
Slight correction: low temperature conductivity declines because phonon wavelengths get so long that they approach the size of the crystal, getting surface effects etc. The conductivity scales as ~T^3 near absolute zero. journals.aps.org/prb/abstract/1…
