I have worked on that problem with the old DEC and few others since. At the time they said that add on cost should not be above $10 (or $30 at retail). Technically speaking, a simple TE module cannot pump much more than about 10 Watts per square inch (that depends a lot on the temperature gradient on the TE module, the greater the gradient the worst the performance). I actually resolved the problem of the limited amount of heat that can be pumped from a given TE footprint as well as the reduction of the COP (coefficient of performance) of TE's in US patent #5,232,516. However, Olson (who was then running DEC) had a simple philosophy, Digital is not in the "plumbing business", and that device requires a minimal amount of "plumbing" (g). Can it work? Sure, if the power needed to be transported is less than 15 Watts or so, at 75 Watts, which is what high end overclocked CPU work at (when overclocked), I doubt it.
By the way, there is another small system (though, if they have the TE under CPU control it is easily controllable), when you cool the chip below ambient, you may get condensation (for instance, if the TE still works when the CPU is relatively quiescent and thus does not dissipate much power) which could short the densely packed contacts. I have solved that problem as well, but could not find anyone really interested in solving that problem, so I did not even file a patent on that solution. These two innovations come under the category of "Solutions looking for problems" (the nemesis of any inventor).
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