My girlfriend and I do a lot of weekend cruises in and around Tampa Bay all year long. We do prefer to spend the night in a marina during the summer and get some AC going but there are plenty of cruisers who just use fans and hatch sheets to get some airflow.
I'd say typical summer highs are 85-90 with lows around 75-80. It'll take you a season to adjust though.
Definitely do-able and don't let the mosquitos scare you. I'm from Minnesota and they are at least a 100 times worse there in the summer than in Florida.
IMHO best times are March April May and September October November.