iMac fan runs continiously

I have no idea but give this a try:  How to reset the SMC of your Mac - Apple Support

As iMac have been produced without interruption since 1998 in five broad families and easily hundreds of variants. how about sharing your iMac's sub-model, the part with a year and sometimes modified with Early, Mid, and Late. That can be important. For example, I've seen a lot of reports of hard drive fan issues in 21.5-inch, Mid 2011 iMacs.

The sub-model is easily available from "About this Mac... in your Apple menu:

When resetting the SMC it is wise to disconnect all wired peripherals including hubs, EHDs, scanners, printers, cameras etc. Also for a SMC reset to be effective please do the reset 3-4 times back to back as it does not always work the first time.

If the resets do not work, that means you may have a hardware issue, in that case please take the computer to your local Apple Authorized Service Provider to have it diagnosed and serviced.