Onan 7000 generator

I don't have one but, a couple days ago someone posted on a similar problem with their Onan.
He checked everything, replaced a few things and still had the problem.
Finally, he disconnected the low oil sensor and it worked. He then replaced the sensor
That's something to try.
Let us know when you find the problem.

High exhaust gas temperatures on a gasoline engine can be caused by a lean air/fuel ratio or late timing.

Hot exhaust can be easy verify by infra-red thermometer.
Even if you don't own one already, they can be bought for $10, or $29 for one with laser pointer.
Check for banana in tailpipe ;)

Look for a dirt dauber nest in exhaust pipe. Or some kind blockage. Im just guessing here . What does the onan manual say about exhaust temp. My 7000 is so old it doesn't give codes. There are also plugs screwed into exhaust that are to be taken out and then run the generator to blow out carbon build up out of these ports then plugs reinstalled.

My old Onan 7000 has a winter/summer setting on the carburetor, and running it in winter mode in the heat will produce the faults you indicated (mine has no code LED, just a Mark 1 owner's ear).