I'm struggling to get a clear understanding of why heat flows from hot to cold. I understand that temperature reflects the average kinetic energy of the particles, and that kinetic energy transfers from the hot object to the cold one until thermal equilibrium is reached, but is this transfer at the particle level or only at a macroscopic level? Does kinetic energy average out between two interacting particles or is it just the distribution of energies in the population of particles throughout the whole space (i.e. a statistical effect)?
In general, you will have particles moving at different speeds inside any body. Temperature is determined by the statistical distribution of velocity, but individual particles might have very different velocities. So when you have two bodies at different temperatures, individual particles colliding might exchange kinetic energy in either direction. However, on average kinetic energy will flow from hot body to cold body. So you are right in saying that it is a statistical effect.