It's June and just off the coast of Florida the water is nice. The average Caribbean water temp is 81°F. According to NOAA (S.East Coast) the average for South Florida in June is 84°-85°F which is even nicer. So while a wetsuit would be great, current temps off Florida are survivable for extended periods without a wetsuit.

As hikermor said though, it's a whole nuther thing off the coast of SOCAL. According to the same NOAA site, S.West Coast is in the 60's -- 60°F even off Anacapa Island, 63°-64°F off Oceanside, CA depending on how far off the coast. That's 20F degrees further away than Miami from 98.6 which is going to work against you in short order. Wetsuit is highly recommended.