Random shutdown, overheating GPU or CPU suspected

I bought this iMac used and it works ok for a while, but at some point sometimes 30 minutes of use sometimes a few hours, it randomly shuts down.

At first I suspected a bad HDD and replaced with an SSD and replaced the RAM. I'm using a fresh OSX install 10.10 or 10.11 ... whatever this one maxes on.

When the system shutsdown the back of the case is quite warm to the touch. I thought of replacing the Power supply for this system, but they're difficult to find and I don't like replacing electronics that could kill me (I'm not a whiz with discharing caps and the like).

I hate taking this system apart, replacing the SSD in it took 2 hours, but I'm suspecting the thermal paste on the GPU or CPU are the culprit. Any thoughts?