Target Display Mode only available when logged out

I have a 2013 iMac that I use solely as an external display.

The issue is that for some reason the fans on it spin at full speed constantly and it is quite noisy. I have tried most suggestions to overcome the constantly spinning fans but nothing seems to resolve it.

However...

installing Macs Fan Control does allow me to change the sensor that activates the fans and this seems to solve the fan issue.

However...

I need to be logged in to start Macs Fan Control, but Target Display Mode only seems to work from the login screen. Once logging in Cmd + F2 does not work.

So, is there any way to enable TDM after logging in so that I can use my iMac as a second monitor without having it sound like I am setting next to a vacuum cleaner?