I was looking at a laptop stand project on instructables.com, and someone commented that to cool off their laptop, they reduced the CPU core voltage from 1.2 to .95 volts, without reducing the core clock.

From what I know about overclocking, you often have to increase the core voltage to aloe for higher clock speeds. And you are supposed to increase the voltage in tiny increments, right? Wouldn't this also work in the other direction? If you reduced the core voltage too much, wouldn't you also have to reduce the core clock to achieve stability?

Yes, I would imagine so. Instructables seems to only include about 3/4 of the sh** needed to actually pull the project off successfully, so I think you are right, you could cool your laptop by decreasing the voltage, but you'll probably also have to decrease the clock speed.

Disclaimer: I have no proof of this, just a somewhat educated guess.

It will cause stability if the voltage is too low. To figure out if the voltage is too low use a program like prime 95.