mikveh hypogeum to keep cool - but that obviously isn't the only solution!
The Alcantara Gorge is one of the few places in Sicily where you can swim in cool, natural freshwater. Yes, it's open to the public and our article has directions.
This is a canyon formed by a river running through volcanic rock and other geological layers in the Etna region. Unlike most Sicilian rivers, which have become seasonal run-off streams, the Alcantara has water all year. If you go in search of it, note that in Italian it's pronounced al-CAN-tar-a, not the Spanish way (al-can-TAR-a). Mispronounce it and people who can help you find it won't know what you're talking about.
However, a search with Google maps works with alcantara+me+sicily.