If you go in the morning, as soon as the gardens open, the weather isn't too oppressive. Late afternoon can be nice, too if it clouds over or the sea breeze kicks in.
Flowers - lots of wonderful summer flowers blooming now including gingers and Canna, a lot of flowering trees, hibiscus and orchids of course. You can visit our botanical gardens here once a month all year round and see different plants in bloom each time. It's an amazing show.
The only thing that might be a bit disappointing at this time of year are roses - they tend to bloom smaller flowers, and go from bud to blown in a day or two because it's so hot, and doesn't cool off at night. September through May they are magnificent. The Ringling Museum in Sarasota has a big rose garden, and there are some scattered around at Marie Selby Botanical Gardens, too. But the rest of the gardens will be more impressive in summer.