We usually visit in the late afternoon - heat of the day. It's much cooler than walking the pavement around the rest of the park, so I wouldn't worry about heat. Tons of shade, surrounded by water with a nice breeze. We bring a picnic and eat an early Supper at the chairs and tables set up by the closed 'Aunt Polly's.' The island closes before sunset, so keep this in mind!
At the end of one of the trails, there's a cabin with a covered porch, rocking chairs and checkers games. Nice spot to cool down. And this island has washrooms with no line up - a huge perk for families!!
It's just an awesome place to explore with kids. No real safety tips. If you stay with your child, you'll have no trouble.