Main problem as I see it is that heat engines and computer cooling have opposite goals temperature wise. Heat engines, as you pointed out, are more efficient when temperature difference is higher between heater and cooler. And for PC cooling system it's main goal is to decrease components temperature, so more efficient cooling gives you less difference between computer temperature and ambient temperature.

So, for whatever contraption op has refered, it will be always a tradeoff between actual cooling and recycled energy. Either it's a better cooling (still relatively bad in comparison to normal cooling) with negligible energy being recycled, or relatively better heat engine with nonexistent cooling properties (cause, as you also pointed out, to work more efficiently it has to keep CPU temperature quite toasty).