Heat is the transfer of energy. A particle that has a bunch of energy collides with a particle that has less energy and transfers some of that energy. The total energy is the same. We can perceive that energy transfer as heat.
But as the universe expands there is more space between particles, and less interaction. If a particle with a bunch of energy never collides with anything it will never lose that energy, but the universe as a whole is cooler. Not because there is less energy but because there is more space in which that energy exists.
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