You are going to visit the Grand Canyon at the hottest time of the year. However, coming from New Orleans it's going to be a "dry heat"!
I picked up my 34E in Florida and drove home to California, stopping at New Orleans and the Grand Canyon along that route.
We mostly traveled West on the Interstate 10, until New Mexico to visit Carlsbad Caverns, then went North on the 285, (had to visit Roswell and spot some U.F.O.s!), to catch the 40. It's a very nice drive.
Don't forget to stop at the Petrified Forest and the Meteor Crater in Winslow, before Flagstaff. Sedona is a beautiful nearby attraction! And don't forget Winona, (...a cheesy Rolling Stones and/or 80's Depeche Mode music reference)!