No. Not for adults.
I think the "desire to think" comes pretty much with the meat hardware, or is at least a product of early childhood and cultural influences. My mind feels like a freeway, full of a constant stream of thoughts competing for my attention...and I know several people who self-report being aware of almost no real introspection or abstract thought. (They are almost all "happier" people than me, by the way.)
I do think rationality training can help those with a high intellectual drive get more traction in actually using that drive to produce something meaningful. Part of the reason I like LW is it feels a little like steroids for my brain -- it helps me focus and organize my thoughts a bit. After reading some of the stuff smart people write on here, "regular life" feels like it is moving in slow motion intellectually and I can make good progress.
I think the "desire to think" comes pretty much with the meat hardware
Intellectual OCD. Untidy ideas bother you, and you need to clean them up.
One of the big variations I see between people is the amount of energy they habitually put into thinking, and I haven't seen this discussed anywhere.
General advice about improving health and lowering intellectual friction would seem to help increase the ability to think, and ideas like "take five minutes to consider the problem" adds impetus, but I'm not sure what the general difference is between me and most people, or Yvain and me.
Intellectual drive isn't an unalloyed good-- cranks have high drive combined with low self-editinig, and some types of depression include a compulsion to think about topics that cause misery and/or inertia. Part (all?) of the value of meditation is getting some time off from thinking. Still, increasing intellectual drive would probably be a good thing for a lot of people.
Has anyone found that rationality training or anything else increases the default desire to think?