I plan to use my peltier to cool my cpu (seems to be running hot lately). It's TDP is 35W. Now, I know 35W is not exact, and I'm pretty confident my cpu is running a little above that. I've been doing some research on, well, whatever I could find.
Have you checked to see what temperature your CPU is actually running at, and comparing that to what it is rated to run at? In other words, are you sure that it is getting too hot?
Maybe it did rise in temperature, but I would think that would be due to either:
1) poor contact between the heatsink and the CPU
2) something wrong with the fan
3) fan or heatsink clogged up with dust
My first thought would not be to go out and purchase a TEC, especially if it had been running fine all along without one.
Instead, I would probably pull the heatsink/fan and blow it out with canned air (don't spin up the fan to high speeds with the air or you can make the bearing fail). Then I would test it with a 12 VDC supply to make sure the fan was running well. I'd re-install it (with new heatsink grease or thermal pad, after cleaning off the CPU of any old grease/pad), and verify that the RPM of the fan was proper.
If that didn't work, Id then go out and purchase a new heatsink/fan combo, clean off the CPU properly using some rubbing alcohol and swabs, then applying the paste or thermal pad or whatnot and remounting the heatsink. Done properly, you'd probably see the temperature come right back down to where it should.
I'd also take the time, while I had the case apart, to blow out any other dust in the system (especially from any fans and heatsinks, including the power supply). That's really all it should take.
Instead, you are looking at doing an experiment while increasing the amount of power your system draws in total, with possibly little gain overall. Not only that, but should you cool things down too much, you might see an increase in condensation, and possibly causing shorts or such (all depending on the humidity and other environmental factors).