The previous answer is mostly correct. I'll add some of the finer points here. My background is a recently-retired CPU designer, and I've done the power calculations many times (for server-scale computers rather than for mobile, though they're much the same).
CV2F loss is described reasonably correctly. Remember that an ideal capacitor does not actually burn any power; the power is expended in the "resistor" that is charging or discharging the capacitor. In a CPU, this "resistor" is partially the effective resistance of the transistor that controls the capacitor, and partially the series resistance of the metal wires in the circuit.
As described above, the calculation is exact rather than proportional simply because the "C" is indeed an effective capacitance rather than actual. The "effective" encompasses several factors. First, and most importantly, not every node will switch on every clock cycle -- not by a very long shot. To economize on power (which is hugely important in today's CPUs), CPU design engineers spend lots of time figuring out how to perform calculations while switching as few nodes as possible. Second, the "CV2" is of course simply the power required to charge a capacitor. Not every node in a CPU charges/discharges to the same voltage. This is partially because different parts of the CPU run from different power supplies, and partially because the intricacies of semiconductor physics (e.g., the MOS body effect) prevents some nodes from swinging to their full supply voltage. So, yes, the effective capacitances are typically simply computed to match a prior simulation.
However, an important point was not mentioned. You've no doubt heard of "Moore's Law," by which semiconductor devices scale down in size every few years. One of the unfortunate side effects of this scaling is that, every generation, CV2F power takes up less and less of the total power budget and simple static power takes up more and more. The fancy names for this type of power expenditure are often "gate leakage" and "subthreshold leakage." The bottom line, though, is that this type of power expenditure is insensitive to frequency -- circuits are burning power whether they are toggling or not, as long as they are hooked up to a power supply. As mentioned, this is becoming more and more of the total power budget.
Also note that, for CPUs, this is purely a DC phenomenon. With a very small number of exceptions, CPUs do not use AC power at all.
Finally, a bit more detail on your final question. As mentioned, CPU designers work very hard to make as few nodes toggle as possible. If every node on the CPU ever toggled at once, the power budget would be blown by a long shot. One of the "big-hammer" techniques used quite often is limiting the amount of instructions that are issued. For example, a dual-core CPU might only use one core. Or, any single core that is capable of issuing four instructions every cycle might limit itself to only issuing two. Or (since floating-point computation is very power intensive), a CPU might shut off floating-point instructions for a short time. Whatever the actual mechanism used, there are various ways that the restrictions might be turned on and off. Some CPUs will have the capability of monitoring their effective capacitance on the fly and restricting themselves accordingly. Others might depend on the operating system to read a temperature sensor somewhere and throttle the CPU when needed. In still other CPUs, the power-control mechanism has nothing to do with throttling; instead, they drop both their voltage and their clock frequency. (Note that lowering the voltage of a CPU lowers the current that transistors can deliver, which forces you to drop frequency as well). It is also quite common for an external program (such as the "cpulimit" you speak of) to be able to tell the chip to throttle itself.
Whatever the reason, this throttling will limit the power of the CPU (and hence lower the temperature) for the obvious reasons. It is limiting the work that the CPU is doing, and hence reducing the number of nodes that switch, and hence lowering the effective capacitance. Or, again depending on the CPU, it will force the CPU to lower voltage and frequency, with the same effect.
