Unless you're backpacking in and are extremely weight conscious of how much you're carrying, if you think you might need bug spray, why wouldn't you bring it? Better to have it and not need it then the other way around.
How to stay cool when climbing:
Wake up early and climb from sunrise until it gets hot. Then, take a break through the heat of the afternoon and start climbing again in the early evening.
Hydrate often and hydrate a lot. Sweating will keep you cool up until you hit dehydration (to a point of course). Dehydration is not a fun thing to pair with climbing or the great outdoors.
Make sure a couple of your friends and family members know where you are on this trip and when to expect you back. Have a backup plan in place in case one of you is injured bouldering (how will you get home with a sprained ankle or broken wrist?).
Also, if you plan on trying some really challenging problems, I would recommend bringing a crash pad with you. It could save you some pretty hard landings and let you climb more difficult routes in a much safer way.
Biggest Tip: Bring someone with you who knows the area. Having a resident pro can be invaluable.