Did find June more comfortable than September. We had a tropical something or other pass close by when we were there in September (most busiest month of the year for hurricanes) and there was an unbearably hot overcast day with no wind.
Two reasons to go in September 1) Water is at its warmest around 83-84. 2) Less crowded
We have been twice in September, once in October, once in April, twice in June and 12 times in May although several of those May trips ran into early June. We prefer April and May to all the rest with June next. Yes the ocean is warmer in September but we think it is a bit too warm and doesn't really refresh you like in May. It also seems more humid in September and October to us. This last May the humidity seemed quite low and the breezes were perfect. It actually felt a little cool at times. We will still go in other months if we get the opportunity though. Just telling our favorites not that we would not go then. One of those September trips was because we got an offer from Marriott Surf Club to stay in a 1 BR suite for a week for $600. The April trip was because we bought a weeks rental at Renaissance Ocean Suites on EBAY for the low bid of $440. Give me a bargain and I will suffer through a week anytime.