I studied this option for my pc for a while.
It is possible but in general, expensive and very dangerous to your PC.
Here is why:
1.For a peltier to be good it has to be over 200W power, so it requires a PSU of its own.
2. If it fails (stops working) it works as a very good isulator, so it would burn your CPU in seconds, and apart there wont be any warning bout it.
3. It will only work well with a very expeneisve water cooling setup, since it can create a 40 degree diffrence from both sides (means it creates temperatures high enought in the water on your loop to create living organisms, and it keeps your water pump working on high temperature, and that is not good).
4. It requires good isolation (you need to cover all the cpu and area surrounding it in something non conductive, or water will condense around the cpu/motherboard due to low temperatures when CPU is at Idle), meaning you probably wont be able to replace your CPU, thermalpaste, etc ever again.
5. Last but not least, it requires you to be very presice in the mounting, for all the reasons mentioned above.
If all of this dosent scare you away, have fun! It can get your CPU into negative temperatures on idle, and that is comething nice to see
.