I took my kids ages 10, 8, and 5 in July a few years back.
If you know your children, you will know if they can handle the situation.
We never used a stroller and my kids did fine.
We took alot of little breaks, brought alot of water, and went back to our resort some days for a mid-day swim/Nap.
While it was extremly hot and humid, the kids had little personal fans and were fine.
We went for 7 days and in the middle of the week we did a "Do-nothing Day" and let the kids swim, shop in the gift shops and just rest and explore the Resort.
I gave each child a disposible camera to use and this seemed to take their minds off the long lines and heat.
When we had a long wait in a Queque line, we made up little games to play to make the wait seem less long and more tolerable. Pointing out hidden Mickeys and other Imagineering marvels kept them busy as well.
Finding an air-conditioned area every so often cooled them off and kept their tempers down and their spirits up.
While we prefer going in May or October, doing a summer Disney vacation while the Schools are out sometimes is you're only option.
Summer trips are very do-able if you use common sense and know your children and how well they deal with crowds and heat.
Have a great Vacation!