I say this knowing that I may get a fair amount of flak for it, but Indiana Jones is the single most useless movie hero in cinematic history. I love the movies, but really, what does he do? He always seems to merely lead to bad guys to the artifacts they so desperately seek, whereupon they discover that, OH MAN, the ancient object was too powerful for them, dudes, and dissolve (or something). In the new one it's no different; basically Cate Blanchett just follows Indy to the place where she can use the plastic (sorry, crystal) skull, then there's an alien, and it thinks at her too much and she incinerates as a result of "too much knowledge" (probably in this case Derrida's Of Grammatology, or potentially Middlemarch). Nothing to do with Indiana Jones. He didn't actually do anything, he just didn't try to put a stop to it when the villain was getting her comeuppance.
But that being said, the movie was still pretty entertaining. And I can't fault Indy for being useless, I'd do the same if that kind of thing always happened: "You want the skull? Fine, go ahead
Also, I have no idea if this pattern was followed for Temple of Doom, because I've blocked it out of my memory. My babysitter showed it to me when I was 7, and because of that heart scene I haven't been able to hear the words Kali, or Kali-Ma, or even the name Carly pronounced in an English accent, without cringing in fear ever since.