I have done it four times along the Tonto Platform from the Grand View trail to the Kaibab, the Bright Angel, and down to the river.
Never do the Canyon before mid-November and never after the second week in May for a general rule. I have been on a trip to Grandview Mesa and Hance Rapids in which the temps at the river rose to 117?F. We had one death and one air rescue. And that was a strong party of Sierra Nevada mountaineers.
My daughter is the expert. Remember that if you do the full hike it's many miles down and about that many squared coming back (Or so it seems, the difference between down and up) You want to dress layered, That way you can adjust your clothing as the light and heat change. And stick to the established trails, with a group, I would suggest a group with at least one communications officer just in case. Safety in numbers (IF something happens to you.. IE: slip and fall, you have someone to assist you) safety in communications (And radio for air/mountain rescue)
Dress layered is good advice. On one trip, 4 of us went into the Canyon at Grandview wearing shirtsleeves and jeans -- desert hiking is slow and painful in shorts. Three days later we came out on the Kaibab Trail in a driving blizzard. Our apparel had added nylon wind pants, down jackets, gaiters, and mittens. We had to schlepp back to the Village in that blizzard.
We were at the south rim for the first few days of November.
I would suggest that you save your legs and (if you are under 200lbs) let the mules do the work !!? ;D
Unfortunately, Im a couple of lbs over weight so we had to rely on the great bus service to tour the rim instead.
We were going to walk a 1 mile stretch of "unpaved" track at the top of the rim - until we found it was around 2 feet away from the edge, with no rail and a straight drop down.
When walking away from the trail, I slipped on the gravel and fell over. Im glad we weren't on that trail !!
Whilst we were there, we saw an air ambulance come to collect someone.
Ann-Marie commented that it would cost a fortune to get airlifted from the Grand Canyon - and if they ever needed to air lift me from there, did I think they would fly over a couple of times for her to take a few pics !! (she's like that? :'().
Anyway, whilst we were there, the weather was great - nice and warm by 11am and then cooling off from around 5pm
Be sure you have good hiking boots. I know a married couple that hiked down and back wearing ordinary sneakers. Both of them ended up losing every toenail on their feet. [They turned black, fell off, and then grew back.] It was the long downhill trek that did it -- poor support across the front of the shoes meant that their toes were getting jammed into the toe of the shoe step-after-step-after-step.