Any advice given by @ti2d is righteous in my book. He coached me through my first attempt up Whitney (made me feel like a hero for aborting the trip to bring my horribly ill daughter back down) and my second attempt the following year which found me dancing at the summit. Hitting the trail around midnight worked well for us in a couple of ways:
1) it ensures a much cooler hike
2) it's a good way to beat any possible afternoon t-storms
3) coming down when most everyone is still coming up is a great energy boost, both mentally and physically
4) hiking in the dark at first makes for a more interesting hike coming down, especially after Trail Camp. You see meadows, waterfalls, etc that you didn't know existed going up!
The only draw back I found was that the last never-ending 3 miles to the Portal are in the heat of the day.