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The National Park Service provides a great description of seasonal weather conditions, as well as a month-by-month temperature chart on its Grand Canyon Weather page. Take a look!
Yes, by June it will be over 100 degree's F in the inner canyon. Start as early as possible, this is also best for beautiful sinrise colors. If you go to the bottom and back in one day, stay at the Phantom Ranch area during the day and then hike back up in the late afternoon. Its a 5000 foot elevation drop into the canyon, take plenty of water, snacks and your camera. The hike down is easy, but the hike out can be, unless you are a excellent hiker, much harder and strenous. Hike down the South Kaibab trail to the bottom for the best views and sunrise shots, then take the Bright Angel trail back up. It has a water stop every mile and a half to the top once you get to Indian Gardens Campground.
Look for wildlife, big horn sheep, mule deer, ravens,squirrels and maybe even a rattlesnake (rarely seen).
Another way to do the trip down and out is by mule. The way in is about the same, but on the way out the mule will do all the walking/climbing while you are ree to look around and enjoy the scenery...
From a experienced 20 year hiking veteran of the Grand Canyon.