Wow, this is bringing back memories. I did a trip to Corfu, but it was in spring. Later, I went to Greece in July and it was really hot. As stated before the beach was cooler as you can go in the water. One thing we did when we were there was to rent mopeds, which allowed us to get out of town and up into the hills. That's probably a bit cooler than Corfu Town. Here's a good link to a discussion on TripAdvisor about scooter and moped rentals today. And, yes, the advice to be careful on the roads is accurate. One of my friends did have a mishap. We were 19 so we survived it all. I would still rent a moped again.
BTW if you haven't read any of Gerry Durrell's books about his time with his family on Corfu between the wars, they would make lovely beach reading for your trip. Here's the first one, My Family and Other Animals.