You should be able to get samples for whatever material you are considering. Place them in the sun in various colors so you can feel the difference. Depending on your location, sun exposure, whether any shade is available...all these factors make a difference. (Certain types of flagstone might have other issues like its reaction with chlorine water that may factor in). Good luck - there are tones of options!

Certain types of flagstone may, but a muticolor will look great and it won't be scalding. Here are a few photos of some jobs we did. They have tons of color but the colors are that beige/brown that go with a lot of things.

Have you considered using travertine pavers on your pool deck? Travertine is natural stone. It does not retain the heat and it is not slippery. It comes in different sizes and colors. Prices are very competitive.

I have a very light colored flagstone,

and it is flesh-searing hot in the summer. I am in Las Vegas. Stones have been getting 130° to 140° this summer. Wish i had picked something else.

I have ivory/white Shellock cement pavers from Artistic Pavers. I'm in FL, so also hot. I'll get my temperature gun later and see what reading I get on my pool deck.