The place to come to share your technical expertise, or just find out what the little springy thing is that's just pinged out of sight under the work-bench.
My thinking is to always start with th easy stuff.
First thing with the cooling system is check for leaks and make sure there is no air in it. It's easy to drain and refill with correct "antifreeze".
The frame on my old exup used to get really hot, I just put it down to the fact there was a bloody hot engine bolted to it.
I never had any overheating problems in the time I owned it either.
Or you could start the bike and get it up to temp, feel the lower rad hose, if it starts to get hot, the coolant is flowing around the system and the pump is working.