My husband and I hiked to the Wave about 10 years ago when were in our 50s. It was mid-May and the temps were in the 90s but that was the coolest time we could go since we had only his summer break from teaching to vacation. Coming from Florida, we're accustomed to high temps, but the lack of humidity really sucks you dry.
We had water-filled camel-backs, plus several quart bottles of Gatorade each, salty snacks and high protein munchies. By the time we got back to our Jeep we'd gone through most of it but were in good shape. The rangers had warned us to drink before we felt thirsty and we made it a point to stop for a bit of water or Gatorade every 15-20 minutes.
As previously mentioned, there is no trail and following the scattered rock cairns would have been risky because they didn't seem to follow any one route. The crude map was most useful for the landmarks it gave. Even with the route co-ordinates pre-programmed into our GPS we got off once but were able to get back on track quickly because we checked the GPS frequently. We saw only a few other people that day. Most were well-prepared.
The most shade we found was cast by the high "walls" of the Wave itself. An occasional rock "spire" along the way across the slick rock offer some, but it was generally only enough for one person at a time.
Now that we're retired, we'd love to go back in cooler weather. It's an amazingly beautiful place, well worth the effort it takes to get there. However, it isn't for everyone. The problem is that people often overestimate their abilities and underestimate the difficulty and/or danger of the situation. I live on a barrier island and see it all the time. People who drown because they don't think the warnings about rip currents apply to them. It's sad when something like this happens.