U Haul's own ratings system
Hello Erik,
ASU graduate Foy here (BS Geology, Class of 1978). Congrats on the move. I hear Eugene is VERY nice. Not Boone, perhaps, but where else is? Grad school in Oregon, perhaps?
The last time I rented a trailer from U-Haul, admittedly some 10 years ago, they had an exhaustive question list concerning the vehicle I planned to tow it with. Like my online friend glc, I towed with a half-ton rated fullsize pickup, so it was no issue, but it was quite clear they'd have declined the rental if I'd have been attempting the trip with an inadequate tow vehicle, and specifically one which was not itself rated to tow a fully-loaded 5x8 trailer (where each make and model has a maximum towing weight rating identified by the manufacturer). That likely being the case, I'd hope you could easily recover your deposit/rental fee from U Haul, as it seems they were about to rent you a trailer falling outside of their own policies.
And you can trust glc and me when we say: A fully-loaded 5x8 is a LOAD. No way you want to drag that thing from NC to OR with a Camry.
Lastly, it's rare that temperatures in the northern Great Plains are appreciably cooler than the middle or southern Great Plains. It's been over 105 deg in St Louis all week, and Chicago is right up there. Likely Minneapolis/St Paul, too. Your best bet is the shortest route, and don't push the speed. All-day sustained 70-80 mph running in hot weather is a great way to pop a hose or fitting, blow a tire, or overheat and cook your automatic transmission. If your Camry has lived in Boone for a long time, making sure your cooling system is completely and recently serviced is a must. Easy does it--this is a marathon, not a sprint.
Safe travels,
Foy