I put 140k towing miles on a 2008 Highlander. It had the factory tow prep package, which included extra cooling. Even so, as it aged the cooling ability declined (dirt buildup or corrosion or whatever) and the trans temp light would come on during long uphill grades. By then it had 185k on the odometer and since my wife was never happy with the seats, I sold it. But I still sort of miss it. I generally towed no more than 3k lbs (fairly low frontal area trailers also), up to about 62 mph, and I took it easier on the grades both up and down. I kept the 5 speed auto out of 5th gear, which (as coolmom42 mentions) will keep the tranny from frequent gear hunting and shifting; the unlocked torque converter which you get in that hunt between 4th & 5th will generate a ton of heat and that can damage the transmission.
Popups also present low frontal area for low wind resistance, so you should have no trouble at 65 mph. Hitch weight limit is 500 lbs and you will want to check your trailer's tongue weight when loaded for camping to make sure the LP, battery, and gear don't put it over that limit. (But you also want minimum 10% of total popup weight to be on the hitch, to avoid dangerous trailer sway.) If you're hauling a lot of weight (passengers and cargo) in the HL, you could run out of payload; find out what your max payload is and take it into consideration.