Those computers were not made with SSD's in mind, I believe there is a sensor in side that would be attached to the original hard drive to run the fans when needed. With it not there they just run all the time. You can download software that allows you to control the fan itself. I have this on an old Mac Mini that I replaced the original hard drive with an SSD and use it to run a wide format printer I have. I keep the fans on a low setting, don't think it is a huge thing as this should be separate from the CPU fan... I think.
Curious how much all of that cost? The screen I would imagine is a pretty expensive thing to replace. Might have made more sense to look for a newer iMac.
You could try doing a clean install of the MacOS, not sure how long you have been on the install you have now, but that can breath new life into the computer as well.