I don't really like these programs. I think it's better to drop monitor brightness than adjust the color temperature. Better for your eyes and you can see the colors better.
The issue isn't brightness, it's the actual color of the light. The tl;dr version is "blue light definitely messes with your sleep cycle." There's a Wikipedia page about this, with several references at the bottom: https://en.wikipedia.org/wiki/Effects_of_blue_light_technolo... (And I'm sure a search in your favorite search engine will find even more information on this subject)
...and kills your eye cells.