Absolutely NOT. A Thunderbird 1Ghz puts out over 60W of heat, and a 55W heat pump would actually function as a processor heater. You may then think that a 72W would solver your problems, but once you realize that that 72W rating is under no load in a vacuum, and that there are additional heat sources such as resistance in the peltier itself, you are chasing your own tail. If you're aiming for 10C, you'd have a hard time doing it with a 156W peltier on a TB 1Ghz. In the hardocp forums they have a thread under the overclocking and cooling section on various q and a's, and many good links are recommended there for extreme cooling (phase change, liquid cooling, TECs, etc). You should give it a look. To be perfectly honest, peltiers are for extremists who do their homework who are looking for that extra few percent (a 10C drop in temperature only results in about a 2-5% increase in performance for most types of transistors). You don't sound like one of these people, even though you might eventually turn out to be. Peltiers though, by their nature, are very dangerous. The condensation they can potentially cause can destroy components through shorts, if the peltier should for some reason fail, it doesn't conduct heat through it very well without power applied, so it will likely fry the chip, etc. More power to you for asking, but do your homework and be careful.
3C2X1(<b><i>Genius</i></b>).
Even though I'm a stranger, at least my average post is intelligent!