My brother did this. He bought an ~1600+ athlon and plugged it into his system. He didn't realize when he bought it that it wouldn't come with a heatsink. He wanted to know if the motherboard and memory worked however, and decided to boot just into the bios to make sure everything was right. He told me it didn't even finish detecting the IDE drives before the computer shut down. When his HSF did arrive, he discovered that the CPU had fried itself, and had to buy another CPU.
I agree with the monkey, In a longer word, don't.