Start at sunrise. Ride as far as you can while you can stand the heat.
Look for diners and libraries to hang out in during the heat of the day, and ride a few more hours late.
Look for warmshowers hosts, fire stations, and churches that might let you sleep in AC.
Catch a bus to about Wichita. One more week of heat, and a week of acclimating to altitudes at the same time, and you'll be in the Rockies. It's drier there, or at least the humidity isn't so oppressive. If you can swing it, ride back to Wichita when you hit the ocean and come east, maybe it'll be cooler in September.
Drink lots of water. Have a drink now. Try a V8. Look for Nuun, Endurolytes, or plain old salt pills; or salt your food if you start to notice you need it. Feeling totally wiped out in the morning is one sign for me, and a raging thirst at the same time you just emptied your bladder is another.