In the not-too-distant future, we'll hit a limit on how small we can make transistors. The logical next step from there will be to starting building up - moving from chips that are almost completely 2D to fully 3D chips. When that happens, we'll have to figure out a way to cool them. Unlike with a 2D chip, you can't just stick a big heatsink and fan on top because it would only cool one surface, leaving the bulk of the chip to overheat. What you need is a network of cooling pipes distributed throughout the chip, almost like a biological system.
I suspect these pipes would work best if they go straight through the chip and out the other side. At small scales, fluid is very viscous and trying to turn a corner would probably slow down the flow too much. So suppose you have a cubic chip with lots of tiny pipes going in one face and coming out the opposite face. The next problem is that, if the fluid is all moving the same way, one side of the chip (the "incoming fluid" side) would get much hotter than the other. The effect could be mitigated somewhat by having some of the pipes flowing in the opposite direction. Ideally you'd want fluid coming in on all 6 faces to maximize cooling. Another possibility is pipes that split up within the chip. A wide pipe of cold fluid will have a similar effect as several smaller pipes of warmer fluid (the increase in fluid temperature is offset by the extra surface area). It would be an interesting puzzle to try to model the heat flows and come up with optimal pipe configurations. In doubling the side of the chip, one probably has to increase the proportion of chip volume dedicated to cooling by some factor 
For most efficient cooling, one would probably want to take the cooling fluid from the CPU and any other hot parts of the system and compress it (just like the coolant in a fridge), allowing it to expand inside the CPU. Then rather than having lots of noisy fans one has one noisy compressor (which would probably be easier to acoustically isolate - maybe even by putting it outside). Fans are a big problem for noise and reliability - my main desktop machine (at the time of writing) has five of them, of which two have failed and a third is on its last legs.
Another major problem that will need to be solved is pluggable cooling lines. People expect to be able to build their own computers, which means that it must be possible to plug together a CPU, motherboard, graphics card and cooling system without an expensive machine. That means we'll need some kind of connector for plugging the coolant lines from the CPU (and other hot components) into the cooling system. Ideally it will be easy to connect up and disconnect without the possibility of introducing dirt or air into the coolant lines, and without the possibility of coolant leaks. I suspect that whoever invents such a connector will make a lot of money.