Why does energy preferentially spread out in an isolated system?
It has to do with increasing the entropy of the universe.
The modern definition of entropy is that it is the extent to which a system is able to disperse its energy. Energy (such as heat!) likes to spread itself out, so that as many states as possible are occupied with the least amount of energy.
Imagine you have a set amount of water (energy) that is able to be poured.
If you poured exactly the same amount of water (energy) into 8 glasses (orbitals), each glass (orbital) would have less water (energy) than if you poured the same starting amount into only 4 glasses (orbitals).
And as every element, molecule, and subatomic particle prefers to be as low in energy as possible, the spreading out of energy is natural.
And this spreading-out increases the entropy of the universe, in accordance with the second law of thermodynamics.
Given that cold is lack of heat, heat traveling towards the colder regions is precisely the dispersing of energy we just discussed.