Color temperature is critical component of how we perceive a photograph or a slice of film. (It's that whole "white balance" thing we nerds are always blabbing about.) As this video explains, we often don't even notice the ways in which an image's color temperature affects us. When directors are playing with color, they're playing with your emotions.
The video from FilmmakerIQ is actually an in-depth tutorial on the science of color temperature and how today's conventions for white balance came to be. But its analysis of the Cohen brothers' Fargo and Spike Lee's Do the Right Thing is accessible enough for any layperson. The former uses blue, "cool" color temperature to evoke the cold North Dakota winter, and the film's icy personalities. The latter uses red, "warm" color temperature to evoke the boiling summer heat in Brooklyn, and the brewing racial tensions in the film. It'll make you look at all movies differently forever.