Honestly even though method and amount has an affect on temps, there's more at work here than the way you spread the thermal paste.
Even on the stock cooler, it shouldn't be reaching those temps, I don't think it would even go that high if you bought two tubes of AS5 and squidged the whole of both onto the CPU, you'd just get a whole ball load of excess around the socket.
Thermal compound just bridges the microscopic gap between the metal on the CPU and metal on the heatsink. A good paste with a fair amount of conductivity is pretty much all that is needed. Application methods and brand are really considerably over examined imo.
With that said I like the dot method (eh, figured I'd add to the method conversation).
I'd be willing to bet your (Stock?) heatsink is the fault, especially considering you wern't running a stress test, or anything too demanding at the time. Have a look in your case and check the fan is running correctly.
Check that neither the heatsink or its fan is clogged full of dust.
And my personal bet, check that all four clamps are how they should be. I've dealt with an issue like this before where someone's computer (allbeit an old one) had one of the clamps that had broken/came loose and caused it to shut down immediately upon booting.
It definitely sounds to me like a contact issue with the heatsink. With that said it is still seemingly in contact, otherwise you would shut down immediately. Still very very borderline. Have a good look at it, press down on each side and make sure there's no lee-way each time you do.
Heck, go as far as picking the damn mobo up using the heatsink, if it flings off one side then there's your problem.
Furthermore, if your fan is working correctly, does it sound like an absolute jet engine?