Yeah... Warmer is kind of mixing metaphors since warmth is just a statistical aggregation of stuff moving around. The point is that photons result from electrons changing energy levels and disappear when they hit an electron and change its energy level. A big change makes a high energy photon which might bump into an electron, resulting in a higher energy electron and a new, less energetic photon. This keeps on happening.

Seen purely as electrons -- one electron had a lot of energy, now a lot of electrons have a little. Seen purely as photos, one photon had a lot of energy, now there are lots on very low energy photons.

Overall, the collective term for this is entropy -- over time we get fewer opportunities for big photons to get created, until it's all small changes in energy and small photons -- total entropy -- and everything is background radiation.