Cycling base layers in warm weather?
Many of these claim to make you cooler (temperature, not social standing :-)) but whether they actually do or not is another matter. Some fabrics can certainly feel cooler to the touch, and thus may make you feel cooler when riding - which could give you a psychological performance advantage - but whether they physically help cool you down is another matter. Finding information on the actual technology and any sort of scientific testing is difficult.

I ride in Florida and the temperature range can sometimes go from cool in the morning to very hot by afternoon. I've worn UnderAmour Heatgear base layers to keep warm at the start of a ride and found them to be fine when it warms up and they help to wick away sweat if you're not wearing a tight fitting jersey. However that's only up to a certain temperature. Once it gets beyond that I found it just makes you hotter.

Another reason may be for sun protection. Many cycling jerseys are so thin they don't offer much.

Some base layers offer a compression fit, too. Again, companies market this as performance enhancing. Whether that's true is entirely subjective, IMHO.

Lastly, (and if you choose to wear a base layer because of this then you may want to practice riding more) they offer some physical protection. I hit the deck at 25 mph once. My jersey was torn to bits and my skin underneath would have been too if it were not for that fact that I was wearing a base layer that came away relatively unscathed. (The weather was warm enough that I didn't need the base layer, btw).