I sit quietly and imagine an air vent with a wedge in the middle. The warmer particles are persuaded to go to the left side and colder ones go to the right. Air isn't uniform, some of the particles are high energy, others are low energy, the temperature is the average of all the particles present.
Is there a way to separate the hot and cold air particles in the air without using much energy? I don't know. Peace comes to those that ponder.