Cool or warm white has nothing to do with the heat range of the lights. Leds run cool compared to other lighting.
"cool white" simply means a pure white light.
"warm white" has a yellowish tinge to the light that it emits.
I'm about to embark on a set of warm white interior Federation lighting. I am betting on that, but give me a month or two and I should be able to demonstrate some effect... I hope...
Cool white LEDs typically have a bit of a bluish tint to them.
“In the beginning the universe was created. This made a lot of people angry, and has generally been regarded as a bad move." Episode 5, The Hitchhiker's Guide to the Galaxy