We know that temperature is proportional to the average kinetic energy of a system. We also know that temperature is not the same as energy because the temperature is intensive while the temperature is extensive. This lead me to think that temperature was some sort of energy density, like how density represents the "average" mass over a volume. However, we cannot express Kelvin in terms of Joules. So if temperature is not just an intensive version of energy, what is it really? How can we link entropy's connotations with disorder with the units J/K?