Failure of the iMac27 inch

Without being able to actually see the iMac and exactly what is happening it is hard to say. Many times being able to accurately assess a computer requires seeing all the subtle sounds & behavior which can help lead to clues to what is actually happening. A bad GPU is certainly one possibility especially for this particular model and a failing power supply or hard drive are other very likely possibilities. If the iMac can stay running long enough, then you can try checking the health of the hard drive by running DriveDx and posting the complete report here using the "Additional Text" icon which looks like a piece of paper. If the iMac won't stay booted long enough, then booting from an external drive may be an option to assess the problem with the iMac. If you don't have a bootable macOS external drive, then I can provide instructions for creating a non-macOS boot drive capable of booting & testing the iMac and its hard drive.

Have you blown the dust out of the intakes lately?

What temperatures does this App report? Especially the GPU.

This App can be used to speed up the fans, all my iMacs would be dead without it.

Never ever ever drop fan speeds below the speed that the Mac itself is calling for.

MacFansControl…

https://www.crystalidea.com/macs-fan-control

With the information you provided it is most likely a power supply or Logic Board issue.

The 2011 model had a known GPU issues.

If the computer is attempting to actually boot part way with a progress bar, then fails it could be an OS issue, file system issue, or possibly a failing drive.

While I have seen bad hard drives power off a computer many times, usually it doesn't require an SMC reset as you are describing. However, recently I've been finding the oddest behaviors with Apple's more recent Macs so it is very hard to say.

From everything you've posted I would suspect you have a bad power supply or a bad Logic Board. I would suspect the power supply first since it is the least expensive part plus maybe it is causing the errors shown in the hard drive's health report since usually when there are Uncorrectable Errors you will also find Reallocated Blocks or Events, but your drive doesn't show those other errors. Plus without a good power supply none of the other components will run properly either and a power issue could affect the SMC located on the Logic Board. Plus the power supply takes the brunt of the damage with poor or dirty electricity.

If you do get the iMac repaired, then you will want to monitor the hard drive's health to see if those Uncorrectable Errors (or any other drive errors) are increasing which would definitely indicate a failing hard drive.

Be sure the cloth dos not impede the exhaust vent. Things are crowded enough back there already:

[image from OWC (macsales.com)}

What I'm thinking, though it easily could be something else...

Normally keeping it under 50° C. would be fine, but years of running at say 70° C will weaken the GPU solder connections & it can still fail as it warms up.

I admit to a lot of conjecture on my part.

The hard drive has 18 Uncorrectable Errors reported so this hard drive appears to have a problem.

DriveDx has a short free trial period. DriveDx does a decent job assessing the health of a traditional hard drive, but doesn't do as well when assessing the health of an SSD although if the health report of an SSD from DriveDx is examined by a knowledgable person it can be useful in troubleshooting. For the purpose of troubleshooting here the free trial period of DriveDx is more than sufficient:

https://binaryfruit.com/drivedx

Those temps aren't too bad. of course the cooler it is the longer it'll last, I'd at least get a small fan to blown on the back to help cool it.

What do you mean by " what is the minimum speed of the fan?"