A Fusion drive is in fact two physical drives (a HD & a SSD) which via software is linked to look like one drive to you.
Yes, you could add-in a SSD and configure your current HD & new SSD as a Fusion drive but that doesn't solve your overheating problem.
If you want similar speed of a Fusion drive you could install a hybrid drive which is a single SATA HD with a built-in SSD (just swapping your current HD out).
Have you tried installing a temperature & fan monitoring app so you can see why its over heating? I would start there.
You are aware this version of iMac has a special HD which has an internal temp monitor. If you swap it out the HD you need to deal with the temp & fan control system.
Given the fact the system is working only shutting down when it over heats I think there is a good chance you might have a simple problem here.
Can you give us the make & model of your current HD and if it's one made for Apple or a third party drive.