replace the cmos battery a brand new one and clear cmos settings to see if a cmos reset can quiet cpu fan.  if cpu fan still loud, consider replace it.

it is likely due to a problem with the fan itself. You can try cleaning the fan to see if that fixes the issue. If not, you may need to replace the fan.

Hello Adam,

Your optiplex is either 1 of the following:

Temperature sensor is Malfunctional, or your BIOS settings are setting the fans to MAX settings.  

Your BIOS settings can be changed, Although messing around with the BIOS is EXTREMELY risky so I would recommend looking at a tutorial. 

If you believe your PC is Thermal - Throttling make sure to Download Speccy its a app that shows all of your temperatures.

Good luck with your computing journey,

James

See if you can throttle CPU to 99% and see how it does.  Throttle it back to 100% and see if problem stays away.