There is essentially zero shade cover on the island to protect you from the sun, so pace yourself and bring a good wide-brimmed hat. And lots of sunscreen.
There are only two consistently reliable sources of water on the island: (1) Santa Rosa Campground and (2) Clapp Spring. So prepare to carry LOTS of water with you. A good rule of thumb is minimum 5 liters/day per person.
To avoid the heat, you might try night hiking. The temperature is ideal after sunset, there are no large animals to worry about (just some cute little foxes) and it's pretty sweet hiking by moonlight.