Overheating

You've identified the cause of the overheating.

Oh my my! As typical for GM, the engineers have come up with an unnecessarily-complicated circuit. It involves three fan relays and two fans. Rather than try to devise a list of troubleshooting steps that would even confuse me, I think it would be more effective in this rare case to test some parts individually. That is normally the least effective way to do it, but we have to start somewhere.

First, if you understand what I'm describing, unplug the two fan motors, then use a pair of jumper wires to hook each one directly to the battery to see if they run. You can also check fuses # 38 and 39, both 30-amp in the under-hood fuse box.

As an alternative, you can bypass fan relay # 1 to see if both fans run at a slow speed. You can do that by popping its cover off, then squeezing the contact, or by using a jumper wire or stretched-out paper clip to jump two terminals in the socket, but I can't tell from my diagram which two ti connect.

My concern here is there are two fan circuits that can each run independently, and they run together for the slowest speed. It is unlikely both circuits have failed, so once you tell me what happened when you connected the motors to the battery, we'll have to determine what could cause both to not work.

Before you waste a wole lot of time trying to fix something that may not be broken you need to be aware that these fans aren't programmed to come on until approx 226 degrees. Most people think that is a problem but it definitely is not. That is exactly the way they are supposed to work. It has 3 relays because it is a 2 speed system.

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Cheers, Ken