I wouldn't worry so much about an early start, except for the first switchers out of the portal, which face east and catch a lot of sun no matter what. Better yet, plan on taking it slow and steady, lots of breaks in what shade does exist, good hats and/or bandanas that can be soaked and worn around the neck or head to promote cooling.
There are really two long stretches of exposed hiking: the switchers above the North Fork cutoff and the stretch headed above Mirror Lake. But, if you plan on nice breaks, where you focus on munching and drinking, it's not that bad.
I always enjoyed starting a bit early to enjoy sunrise from the high switchers, which I think gives the feel of actually being part of the Range of Light.