now i know this wouldnt be that hard. using air conditioning process as a way of cooling air, mabe even liquid at the same time and cooling air as a by product.
an air conditioning system work almost the same as a liquid cooling system, but focuses on cooling more then just circulating.
this diagram shows how it works.
if you can make this miniature, you have yourself a below room temp. cooling system.
making this smaller shouldnt be too much of a problem, since the only reason why its so big and bulky, is the fact that there trying to cool a entire room. where trying to cool a much smaller computer case.
and it doesnt all have to fit inside the case, it could also fit behind or partialy inside, just like some liquid cooling systems.
all you basically need is:
A compressor
An expansion valve
A hot coil (on the outside for dispersing heat)
A chilled coil (on the inside for cooling air)
Two fans
A control unit
(i drawed that myself by the way, lol....
)