If you start on the remote islands of the Outer Banks of North Carolina you'll feel right at home with their Hoigh Toider accent. Unlike others - I'd recommend East to West. You mentioned temperatures. If you start in early May on the east coast you can get thru the Great Plains by mid June before it gets obscenely hot. Then you'll catch the Rockies after the last spring snowstorms and wildflowers in the high country. Remember, it can snow into June - and deep snowpacks don't melt out until July.
I've ridden both ways - a half dozen trips - and there is little wind advantage either way, but there is a definite seasonal advantage East to West. Plus easterly winds are characteristic of cool/rainy days while westerlies of hot dry days. If you are riding East to West you have a tailwind on chilly days and a headwind cooling you down on hot days. West to East you get a headwind on chilly days and a wind pocket on hot days.
What's more, you can take in the colonial/English region of the U.S. first and save the stunning Western scenery for dessert. Have a great trip.
John