The average yearly temperature in Destin is 78 degrees with an average high of 91 in July and August. By contrast, the coldest month is January: lows can reach 31 degrees. The hottest month, July, also gets the most rain. The best time to go is in the spring, March and April, when temperatures are in the 70s and it is sunny almost always. 

While the spring is nice, you run the risk of cold weather and can't really swim.  May to June is the best time for swimming.  The water is nice and warm and it's not too hot.  July and August are really hot.  September is another good month and you can get reduced rates.