Q: Temperature gauge erratic/ rpm erratic

Most likely this is a problem with the instrument cluster. Even so, I would make sure your vehicle isn’t actually overheating. The best method for doing this is with the use of a infrared temperature gun. They aren’t cheap, but there isn’t another way to be absolutely sure. You can feel the upper radiator hose to see if the thermostat is open. The hose will be hot if the stat is working properly.

The tachometer and the temperature gauge rely on the instrument cluster module for the proper information to display. GM clusters are common failure items, so I am certainly leaning this way. I am not sure what you mean by the PCM/ELM seams hot. Modules will often become warm when the car is running. Although, if these problems begin only when the PCM gets up to operating temperature, it may have a problem. Although, PCM are rare to fail, so I would do every test I could imagine before replacing it.

I recommend having this looked at by a certified technician, such as one from YourMechanic, as one of our mobile technicians can come diagnose a potential overheating issue and help you pinpoint the issue with your gauges.