A heat sink kinda works the other way, taking heat from something and passing it to the air passing over/through it. +1 Overshocked. The air will be just slightly warmer from having passed over the fan motors so ther'll be no help there.
That said, cooling the charge going into the system isn't a bad idea. A cooler environment will improve the cooling of the chipset, CPU and GPU. The problem is HOW?
Maybe some peltier arrangement with the pelt sucking heat from the "heatsink". You'd need to get rid of that heat somewhere too so you're probably looking at another heatsink on the other side of the peltier and a fan pushing air over that too.
No, I really think that phase-change or water cooling is your best bet if the ambient temperature is high.