Some stray questions:
1. How is your external monitor connected to your computer?
2. Do you have any other external devices connected to your computer?
3. What things have you added to your computer, since you purchased it? More memory? Changed hardware?
4.
It is not a thermal issue.
Why are you sure of that?
The only thing that I know of, that will cause an "instant shutdown", is a hardware issue.
Most commonly, a problem with the power supply. Less frequently, a thermal issue, peripherals, etc.
In this case, given the symptoms, I suspect the power supply.