I don't know if the newer motherboards do this or not but if your CPU fan falls below a certain RPM I think it was 600 rpm the motherboards would immediately shut down.So it could be a failing CPU fan,Power supply overheating or CPU overheating because of dirt.Or possibly a bad speed sensor in the CPU fan,I've had a bunch of the stock Intel Core Duo,Pentium D and Core 2 Quad fans malfunction like this.
If it is still shutting off after you blow it out,I would replace the CPU fan.They are easy to change out and very cheap.I have a couple dozen CPU fans in the closet,If I don't have 1 that will fit your CPU Heat-sink I'm sure some one else may have 1.
Most PCs from Dell,HP,Compaq ect. ect. Will not shut off because of heat.They will keep running and burn them selves up.Because the Bios in the Box store PCs does not have an Overheat Protection option.Here's an old Pic of a Bios with Overheat Protection.