In that spirit, here's a poorly-researched crazy idea that would explain everything: the most important limit to cognition, both in terms of IQ and in terms of willpower, is waste heat from the brain.
The brain is metabolically active tissue that produces a disproportionate amount of the body's heat (about as much as all skeletal muscles combined). It's also the most heat-sensitive organ in the body. It only survives at all by a complicated system of veins that transfer brain heat to the skin and nose.
According to the academically mainstream "radiator hypothesis", the development of this venous system was what allowed us to evolve from apes into humans. Apes with ape-level brains were already kind of at the limit of their ability to eliminate waste heat, and so couldn't to evolve larger brains without frying themselves. When ape-men started walking upright and lost their fur, this changed the amount of the head exposed to the sun and changed facial circulation since all of a sudden gravity was draining all the blood down. This allowed more efficient venous waste heat removal, and suddenly there were no waste heat constraints on the size of brains. Brain size started ballooning over only a few million years.
Now recently there's been a lot of talk over people finally discovering a plausible reason for yawning: it cools the brain by pumping the venous system and heat exchange with the yawned air in the sinuses. Quite a few studies have found good evidence for this: people yawn more often when it's hot, people yawn less often when it's so hot that air temperature is above body temperature, and brain temperature goes down after yawning. So yawning, too, seems to be part of brain thermoregulation.
But as far as I know, the thermoregulatory theory of yawning doesn't bother to explain why we yawn more often when we're tired. However, it seems really interesting to me that the other things we do when we're tired to wake up - stretching and splashing cold water on our faces - are both thermoregulatory measures and particularly brain thermoregulatory measures. Stretching pumps the countercurrent systems in body veins, and splashing cold water on the face (or taking a cold shower) cools the face, which cools the facial veins which in turn cools the brain. So between the yawning, the stretching, and the cold water, everything we do to feel a little better when we're tired involves brain cooling. Why?
[EDIT: alicorn24 points out that mammalian diving reflex is at least as good an explanation for the invigorating effect of cold water.]
Well, here's another article: Head cooling cap eases insomnia, study finds. If it's true and not one of the Ten Million Promising Medical Findings That Disappear When You Investigate Them Closely, it shows that a lot of insomnia can be treated much more effectively than any existing methods just by effectively cooling the head (and therefore the brain). It further attributes this to the frontal lobe, which it says is the most metabolically active (and so most susceptible to waste heat) and which is most active in insomniacs.
The frontal lobe is responsible for executive control/willpower type tasks, so we can imagine a scenario where the insomniac isn't tired, but is trying to force herself to lie down and stop fidgeting and count some sheep. This takes a lot of work from the metabolically active frontal lobe, generates a bunch of waste heat, and there's a ceiling on how hard the insomniac can try this because the brain wants to avoid frying itself. Use the cooling cap to get more waste-heat-removal ability, and the frontal lobe can work harder at suppressing the rest of the brain and getting to sleep.
When you're tired, your brain really wants to go to sleep. When you tell it "Not now, brain! I've got to attend lecture!" you're using your frontal lobe's inhibitory/executive control/willpower functions in an equal but opposite way to how the insomniac uses hers. If you're really tired, you may be overclocking those functions and generating dangerous amounts of waste heat. Either one of two things will happen: your frontal lobe will give up and you will fall asleep, or your brain will overheat and you'll need to dissipate the heat through yawning, stretching, cold water, etc. Now we understand why you yawn more often when you're tired.
(this also explains, almost as an afterthought, why we yawn more often when we're bored. It takes willpower and conscious control to keep listening to the boring lecturer, and that generates waste heat. If you're both bored and tired, you end up like I did this morning: yawning so much it gets embarrassing.)
I predict - and I plan to test later when I have more free time - that cooling the brain in some other way, maybe like the cooling cap in the experiment, or running a constant stream of cold water over your face - would allow people to be less tired and have more willpower. It might even make them smarter.
Speaking of smarter, today I learned about the latitude-IQ correlation; that is, people on average have significantly higher IQs at latitudes nearer the poles (they also have physically larger brains). Kanazawa, continuing his trend of never saying anything I agree with, tries to explain this by positing that the difficulty of adapting to a cold climate forced people to evolve greater intelligence.
I have a few problems with this theory. For one, it's a bit group-selection-y. If I evolve a high IQ and, after years of dedicate research, discover the jacket, then this helps me survive in a cold climate, but once the jacket spreads to the rest of my tribe and culture, unless primitive Neanderthal tribes had some primitive form of copyright law I'm not going to benefit much from it.
For another, this suggests that all the people in warm climates were just hanging around going "Yeah, we could evolve more intelligence if we wanted, but there just aren't enough challenges to make it worth our while." But that totally flies in the face of the Machiavellian Intelligence Hypothesis, the idea that there's a runaway selection effect for intelligence because it helps gain status within the group; people should always want more intelligence if they can get it. It would be really strange to think there there's some high-IQ mutation simple enough that high-latitude-people could get it in the 30,000 or so years since they started living in high latitudes, but that low-latitude folks never bothered to pick this low-hanging fruit.
Unless they couldn't mutate, because the mutation only works in cold climates. If the first few million years of human evolution were driven by increased brain size as a reaction to bipedalism giving increased heat-dissipation opportunities, maybe the last few tens of thousands were driven by living in cold climates also giving increased heat-dissipation opportunities - that is, the brain, with access to cooler air and cooler venous blood, could work harder before it risked overheating.
Now since high-latitude people have only been in high latitudes for 30,000 or so years (you can gain a few tens of thousands by claiming the genes involved came from exchange with Neanderthals, I guess) this would imply some really fast mutation. But it's still much slower than what the selection for intelligence some people say occurred in Ashkenazi Jews over the past few centuries, and just making the brain a little bigger isn't exactly subtle. I think it's well within the sort of selection that goes on all the time if you believe The Ten Thousand Year Explosion (which I mostly do).
Now, we already know that we can do almost miraculous things to physical performance just by cooling the body. I hypothesize that it may be possible to do the same for mental performance. Not necessarily raise IQ directly: that might only operate on the level of generational mutation - but increase mental endurance, to the point where you don't need to keep taking breaks every few minutes when you're doing something cognitively demanding (I think one reason for those breaks might be to wait for waste heat to dissipate and your brain to cool back down).
I wish I had something advanced like the RTX in the article above or the cooling caps in the insomnia experiment that I could use to test this, but when I get some free time (realistically at least a month from now), I'd like to at least try to test it with something simple like icepacks to the head and neck (I recently ensured excellent access to the emissary veins of the scalp) and maybe seeing what kind of cheap cooling technology is available. In the meantime, I would say watch the development of body cooling technology as well as research into diseases like epilepsy and MS that might have a thermoregulation-related component.
There. That's my crackpot idea for the day. I'm curious to hear how it gets torn to pieces.