The summit's a lot colder than Trail Camp, keep in mind.
Just have some warmer clothes that you can wear in your sleeping bag if you're really cold. And hope that your hiking buddy likes to snuggle.
Last year at the end of June or so, my son, his scout troop and I hiked to the peak via Horseshoe (west side), and hit the peak for the sunrise. It was literally the COLDEST I've ever been. Beautiful experience, and one that my 13 yr old will remember for ever, but I was glad I had a son to snuggle with as we were both FREEZING in the hut, trying to warm up before heading back to Trail Crest. My batteries in my camera were zapped of any power--I had to warm them up under my armpit for about 15 minutes for them to have enough juice to snap a few pics.
Enjoy the trip!!!