Oh, alright, I gotcha. I'm not sure a peltier will work in this application, because all it does is move heat from one side to the other, and it uses a lot of energy in the process. So that means that you might be able to keep your processor at 20c lets say, but you will have to dissipate 300-500w of heat off the other side.
actually, that is not really a proper way to describe it. Here, let me put it this way, a peltier pumps heat from one side to the other, giving you a temperature differential (60-70c max). so if you were to keep the hot side of the peltier at 30c, the cold side would (eventually) hit -40c. Now as the difference in temperature gets larger, the amount of heat moving from the cold side to the hot side decreases. So the closer to ambient you keep the hot side, the more heat you move, simple enough. But the major downside of peltiers is that they are very inefficient in what they do (as compared to phase change systems), but they are much cheaper to make.
Because of the amount of heat they put out, they are only practical on certain applications. If you had a very large water block hooked up to a massive radiator you could use that to cool the hot side of a peltier, but in your application (as i understand it, at least, i could be wrong tho) all you would be doing is introducing a huge amount of heat into your case, and restricting your height even more.
That is not to say one COULDN'T work for you.
if you really have your heart set on using a peltier, i do have some ideas of how you might be able to get away with it, but I'm not sure that it will exactly how you envision it.
No a different subject, I DO have an idea for how you could cool your processor with a height restriction, and it is to use all copper server heat sinks and a centrifugal blower. something like
this but maybe not that one in specific, as it is kinda loud, but is rated for CPU up to 150w.
Anyway, I'm sorry, I don't mean to be all down on the idea, I just don't want you to end up with something that does not work how you expect it to.
-Connor