So I'll just be browsing, doing whatever on my computer, and suddenly the image colour on both monitors will appear to change to the "warm" setting. But in the settings menu, nothing is changed.

Has anyone else had this problem before, and if so, found a solution?

Some monitors have an "economy" setting which changes the screen brightness and "temperature" at times when it thinks you aren't using it.

Alternatively, check if you have any third party programs or the specific website for a "Night-mode" setting - sometimes it's automatic, but I've never heard of one that changes the colour rather than the brightness.