It was a bet with my friend. He laughed at me because he said computers don't need thermal paste (by heatsink thats what i mean') I mean, most do.. but I guess some older ones don't..
So you actually mean with a heatsink and fan but without thermal compound?
It would post. It would run. It would just run hot to very hot depending on the CPU. I did a bunch of experiments with and old Athlon 64 3200+. It ran 10*C hotter without compound. I also removed the heatsink, slowly, during operation. It auto shut down somewhere above 115*C.