I hear that designing the thermal efficiency of such systems is very difficult. I'm not sure why, though, and I am interested.
On the one hand, I bet the heat is somehow a function of the total power in the system. On the other hand, as individual bits are flipped, I imagine the heat migrates around the die.
How does heat move around the die, and how does this affect the cooling of the CPU? Are specific compensations made to accommodate the movement of heat?
All the fundamental issues about the Thermodynamics of the heat sink design are well presented here (make sure not to miss the pretty CFD pics at the bottom of the page).
What's not presented here is the larger flowfield structure inside the computer case. In more recent years, with the push to get CPU speeds at 3+ GHz, there has been more work in designing (1) ducted fans as well as (2) flow ducts into the casing which pass air quickly in and out of the case.
Ducted fans produce more thrust (or move more air) than regular fans, because the duct causes less flow leakage around the tip which happens to be radially-speaking the highest velocity point of the fan. (This is a similar concept to wing tips on planes). So, the blade tip is the place on the fan that can move air the fastest.
Regarding flow ducts within the casing, the idea is to use the Bernoulli effect of a nozzle to accelerate the flow over the heat sink so that it can remove heat as fast as possible. This has especially become popular for overclockers trying to reach speeds of 4+ GHz (e.g. see http://www.overclockers.com/ducts-the-cheap-cooling-solution/).
The desire to produce faster and faster CPU's really have pushed the need to design better cooling systems. Topics such as liquid or nitrogen cooling are not discussed, but are also alternative methods to try to more efficiently cool the CPU, especially for overclocking at speeds above 5 GHz (e.g. see http://www.tomshardware.com/reviews/5-ghz-core-i7-980x-overclocking,2665.html).
Finally, I leave you with something to think about... I once heard the heat produced by a CPU running at 10 GHz is equivalent to the heat of the sun. There is a pretty good discussion on that topic here: http://www.reddit.com/r/askscience/comments/ngv50/why_have_cpus_been_limited_in_frequency_to_around.
The thermal system around a modern processor chip is indeed complicated and a major design focus. For both electrical and economic reasons, it's good to make individual transistors in a processor small and close together. However, the heat comes from these transistors. Some is dissipated all the time just because they sit there with power applied. Another component occurs only when they switch states. These two can be traded off to some extent when the processor is designed.
Each transistor doesn't dissipate much power, but millions and millions (literally) crammed together in a small area do. Modern processors would cook themselves in seconds to 10s of seconds if this heat wasn't actively and aggressively removed. 50-100 W is not out of line for a modern processor. Now consider that most soldering irons run from less than that, and heat a chunk of metal with about the same surface area.
The solution used to be to clamp a big heat sink onto the small die. In fact, the heat sink was a integral part of the overall design of the processor. The package has to be able to conduct the heat power from the die to the outside, where the clamped-on heat sink can conduct it further and eventually dissipate it to flowing air.
This is no longer good enough as the power density of these processors has gone higher. High end processors now either contain some active cooling or a phase change system that moves heat from the die to radiating fins more efficiently than plain old conduction through aluminum or copper did with the old heat sinks.
In some cases Peltier coolers are employed. These actively pump heat from the die to someplace else where it is easier to couple to the air flow. This comes with its own set of problems. Peltiers are rather inefficient coolers, so the total power that needs to be gotten rid of is significantly larger than just what the die dissipates. However, the active pumping action can help, even if the radiating fins eventually are much hotter. This works because the aluminum or copper of the radiating fins can stand much higher temperatures than the semiconductor die can. Silicon stops acting like a semiconductor at around 150°C, and real circuits need some operating margin below that. However, heat sink fins can easily handle much higher temperatures. A active heat pump makes use of this difference.
In the past there have been processors cooled with flowing liquid nitrogen. This doesn't make economic sense for ordinary desktop PCs with today's technology, but heat management has been a important part of computer design pretty much since the beginnings of computers. Even back in the 1950s, keeping all those vacuum tubes from melting each other was something that had to be carefully considered.
