I found the following: We have already seen that the flow of heat through conduction occurs when fast (hot) atoms collide with slow (cool) atoms, transferring some of their kinetic energy in the process. One might wonder why the fast atoms don't collide with the cool ones and subsequently speed up, thereby gaining kinetic energy as the cool ones lose kinetic energy - this would involve the spontaneous transfer of heat from a cool object to a hot one, in violation of the 2nd law. The answer lies in energy and momentum conservation in a collision - one can show, using these two principles, that in a collision between two objects which conserves energy (called an elastic collision) the faster object slows down and the slower object speeds up. I believe there are some configurations in which the hot atoms speed up and the colder atoms slow down. The energy flows from hot to cold, but it's possible that some energy also flow from cold to hot, naturally. But in the end, the flow is like 99% from hot to cold. Am I right or is the statement in bold true, and if so, how can you prove it?