Heat, on a molecular or atomic level, is kinetic energy; fast moving particles are literally hotter. So, if a fast moving particle collides with a slower particle, there will be an exchange of energy. We know from basic physics that force equals mass times acceleration, so when a force is applied to a particle, that particle will accelerate. That is how heat is transferred particle by particle. All of this happens on such a small, sub-microscopic scale, that we do not see the mechanics of it, we just see heat being conducted.
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