My friend had a similar issue, but not the same as yours.
Just for your consideration, this is what I did.
His laptop shut down even when entering BIOS mode. I initially thought it was a glitch with the OS, but shutting down on Bios mode confirmed that it was an hardware issue. So, I cleaned his laptop with an air blower, but the problem remained. I took a closer look at the fan and listen to it. It turned out the fan was not moving consistently. I thought his fan was completely broken, so I took it out and dismantled it completely thinking that he would need to order a new fan. When I dismantled it I found a small ball of dust about the size of a small booger. So, I just cleaned the fan and mounted back on the laptop FIRMLY just to give it a go. And it worked.
Perhaps, the problem was with the fan not being clean. or may be the fan was not mounted firm enough to have a good contact with the CPU.
I know it's not the same case as yours, but why not give it a go if you haven't found an answer?
hope it helps!