Though I am very Techie minded, it's difficult to answer this on a forum.
I presume the PSU has a built in fan.
Unplug everything from it, and see if it powers up and runs Ok. ie, more than ten minutes.
If all's ok, turn it off.
Then plug the motherboard in and see what happens as regards turning itself off.
If all's ok, turn it off and plug something else in.
Trial and error everything. It might be a DVD drive or a Hard Drive causing the overheat/switching off.
Hope this makes sense. Just don't plug/unplug ANYTHING with the power on.
If your capable of changing the PSU, I'm sure you know this already