Fan on my IMac keeps running despite SMC reset. What else can I do? (iMac 21.5 Late 2013) 2.7 GHz Intel Core i5

Using Activity Monitor

• Use Activity Monitor on your Mac
• What to do when a process is using excessive CPU – The Eclectic Light Company
• Runaway applications can shorten battery runtime, affect performance, and increase heat and fan activity.
• Using Activity Monitor Part 1- CPU and Memory
• Using Activity Monitor Part 2- Energy, Disk, and Network

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    If possible, backup your files before proceeding.

1. Shutdown the computer and disconnect all third-party peripherals.
2. Wait 30 seconds before you restart the computer.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally. See How  to  use  safe  mode  on  your  Mac.
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
9. Reinstall a Combo Updater  macOS Catalina 10.15.6  Combo  Update, macOS Mojave 10.14.6 Combo Update, macOS High Sierra 10.13.6 Combo Update, macOOS 10.12.6 Combo Update, OS X El Capitan 10.11.6 Combo Update.
10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.

Continued,

Macs often don't cool enough during sleep, but sometimes it's a 3rd party kext that doesn't like sleep.

EtreCheck is a FREE simple little diagnostic tool to display the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to help people help you with your Mac. It will not display any personal info.

https://www.etrecheck.com/

Pastebin is a good place to paste the whole report if you capture the URL while there…

https://pastebin.com/

Whew, they've changed pastebin & made it harder, but after pasting in, click Create new paste button, then Embed button, then copy the URL...

<script src="https://pastebin.com/embed_js/KuvnghqA"></script>

The important part is...

https://pastebin.com/embed_js/KuvnghqA

Workable but harder for me to work with...the Note tool on the bottom of this editor's toolbar, as shown in the image, to copy and paste the output from EtreCheck. In a Reply before you click post, look for this to add longer texts...

11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.

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