No
Lets put it this way, a Pentium I will get to hot to touch in about 1 sec. A modern processer has smaller pathways, and has more power shoved through it. If the computer cannot shut itself down as the CPU gets to hot, it will literally start to smoke and burn. Get on youtube and search for videos of people taking off the heatsink.
You can hit the power button and have the PSU come of with out the CPU in however and with a device (ohm meter etc) you can test the power. If you absolutely have to have the CPU in, get a fan (and kind [e.g a desk fan, but a powerfull one]) and have it blow on the CPU. BUT DO IT QUICKLY, just a few seconds, 5 at the absolute max, and do it at your own risk.