Q: MacBook Pro fan runs excessively right after startup even after resetting the SMC

Assuming it isn't caused by any third-party utilities gone astray, then I might be inclined to suspect a failed temperature sensor. Run a hardware test to see: Using Apple Hardware Test - Apple Support.

What is your exact iMac model?

That isn't the actual Model. There are hundreds of MBPs out there. Open About This Mac from the Apple Menu to find out your exact model.

Then get the information this way: To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

Didn't the About This Mac panel show anything like this: iMac (21.5-inch, Late 2013). I have an iMac from Late 2013.