The dreaded code 36

Glad you found the problem. I have the same generator and I have had it happen twice that the generator would run for 15-30 minutes and then shut off with the same code as yours. Both times the oil had been changed recently and the proper amount, 2 quarts had been added. In both situations I drained about a quarter of a quart of oil out and that resolved the issue. I know now to only put in 1.75 quarts when changing the oil. I just make sure I check the level often.

Replacing the fuel pump should solve your problem.....

It was the pump.

Yeah, I have a new pump and, on paper, seems a simple job but it's a bit tight in there for my hands so I'll let the shop do it while they look at some others things as well.

It is logical to think that if pump works while priming, then it is not
the problem. However, there is a component in pump that fails when it gets hot (on certain pumps) Airtex does make this pump for Onan. You can get from NAPA. Onan part # is A047N929. From my experience as an ONAN tech (30+years) Your symptoms indicate bad pump, or ...hopefully not....control board. Since pump is 1/4 cost of board, that would be first step. I have had control boards, when they get hot, break down and quit supplying voltage to pump.

As others have said it is probably the fuel pump. One other easy test is disconnect the fuel line coming to the pump, install a short fuel line from the pump inlet to a gas can. You only need 3 feet or so of fuel line. If it continues to run with no symptoms, you may have a cracked fuel line coming from the gas tank. I chased this same issue on my 2000 Onan 5500 for several weeks before finding the cracked fuel line. It always seemed to be worse in hot weather and I thought I was having a vapor lock issue.

Not expensive or very hard to run the new line. Mine had a couple of metal sections on the run and I replaced all of the line including the metal with new rubber fuel hose. I tried just replacing the rubber sections and it would still quit running. I have not had any issues since.

Now that you brought up heat mine has an altitude adjustment. After about 30 minutes on the road mine would shut off. After cooling it would restart. After changing fuel pump (with Airtex by the way) and not having any changes I backed the Altitude adjustment to 2000 feet with it being 3400 feet where I live. Wow, I have never had another problem. A mechanical seat like this happens to be with a screw and an altitude label may not match up exactly. Heat expansion starved my Generator even as I went up in altitude. Might help you too.

It's air-cooled by the way. I did buy a replacement fuel pump (Airtex) as well as an Onan tune-up kit, the fuel and air filters of which I've used. I figured if the fuel pump works while priming, which it does, then it works. It's odd that temperature would be a factor. I'll read up on replacement procedure and see if I can tackle it as I do have good access to the underside.

agree with other posts, most likely fuel pump. Onan has published
service bulletins on this, and these pumps have relatively high
failure rates. Retail price on pump is around $100, and pretty easy replacement if you have access to bottom of genset