I got the impression that D_Malik was using the word to indicate a lack of akrasia: i.e. a perfect ability to undertake tasks believed to be in your best interests, without limitation by boredom, distraction, procrastination, etc.
Isn't distraction sometimes simply a lack of resolve about what it is that one ought to be doing? Does having willpower mean that I am 100% confident in judgments I made at some previous time about what I ought to be doing now, even if I've had new inputs since then (such as an RSS reader helpfully popping up in my tray) ?
For the past few years my willpower has been steadily increasing. If it lasts and I use it to accomplish something noteworthy, I might write a post about it.
Anyway, what should a rational preference utilitarian with infinite willpower do? Assume that there are no negative effects (unhappiness, stress) with using this willpower, and that they can control their emotions at will.
Clearly they should work a lot more, not spend time on recreation (movies, TV, games), stand instead of sitting, etc..
What else? Should they listen to music? Should they keep their muscles flexed 24/7 ? What should they learn, where would they have the most relative advantage? How much time would be worth spending on social interaction?
I can figure out these things on my own, but those questions are important and good ideas are very valuable.