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.
What I'd do during an infinite willpower streak is:
Determine the most important thing I should be working on right now ( "Maximize on big things, satisfice on small things", "concentrate on the high-order bits", 80/20 rule, "What are the important problems in my field and why aren't you working on them?" )
Sit down and work-work-work-work-work while it lasts.
(Alas, my last two-week long streak of infinite willpower ended a couple of days ago, so now I have to go back to regular, limited willpower.)