What does Indy say to the villagers in "Temple of Doom"?

That is one of the things wrong about this movie. While that village is supposed to be indian, those were Sri Lankan people and spoke sinhalese; Native language of SL. How do I know? Cuz I'm Sri Lankan as well.

And to answer your question Indy says "Thank You, Thank you so much" (Isthoothyi, Bohoma Isthoothyi")

TL; DR

There is strong evidence that he says something along the lines of: "Thank you, thank you very much".

Long answer

The script (if we assume it is legit) differs from the scene in some significant points, which seems to indicate that part of that scene was either improvised or rewritten on set.

Some differences:

Script:

WILLIE: (quietly) God, I am starving, but I can't eat this...
INDIANA: That's more food than these people eat in a week. (pointedly) They're starving, too...
Willie looks around at the emaciated faces and feels like crawling into a hole.
WILLIE: I'm sorry, I -- here, please.
She picks up her plate and gently hands it back to the women.

Actual scene: (transcribed by me)

WILLIE: (decisive) I can't eat this...
INDIANA: That's more food than these people eat in a week. (pointedly) They're starving.
WILLIE: Oh, I'm sorry, you can have it.
Willie tries to hand the plate back to the women.
INDIANA: (insistently) Eat it!
WILLIE: I'm not hungry.
INDIANA: (whispering) You're insulting them and you're embarrassing me. Eat it!
SHORT ROUND: Eat it!
CHIEFTAIN: (gesturing) Eat.
The women next to Willie touches her arm, encouraging her to eat. Willie, with a disgusted look on her face, takes a handful of the food and puts it in her mouth.

Now there are some lines in the script that are completely missing from the movie, probably got cut:

The chieftain finally speaks to them --
CHIEFTAIN: You will rest here before you go on.
INDIANA: We'd appreciate that. This was an unexpected detour. We'll have to go to Delhi now and find a flight west.
SHORT ROUND: (smiling) Indy is taking me to America.
All eyes are on Short Round. Puzzled by this strange attention, Shorty's smile fades nervously.

Next follows the part of the scene that you are presumably talking about, Indiana is asking for their help to get to Delhi.

Script:

INDIANA: I'm a professor. I have to return to the university. Can you give us a guide to take us to Delhi?
The chieftain indicates a young villager sitting near them.
CHIEFTAIN: Sanju will guide you.
INDIANA: Thank you.

Actual scene:

INDIANA: Can you provide us with a guide to take us to Delhi? I'm a professor. I have to get back to my university.
CHIEFTAIN: Yes, Sanju will guide you.
INDIANA: (say something in a foreign language that sounds like "Estute, mahoma estute.")

I have to admit that I don't know what language he is speaking, but if you look at the situation, the way he says it and the correlation to the script, it has to be some expression of gratitude.

I looked up both "Thank you!" in Sanskrit and Hindi but could not find an exact match to the phrase he says. So it is either another language or he uses an expression with similar meaning but other words.

The Making of explains that they were shooting with actual natives from the village (around the 12 minute mark) who did not speak any English. I assume Harrison Ford asked them what the line would be in their language and used it for greater authenticity.

I'm sitting in front of the movie right now. The only foreign words he says to the locals in this scene are "Istuti" and "Bohoma istuti", which mean "Thank you" and "Thank you very much" respectively in Sinhala. Are those the words you meant? Or maybe there's an extended version I'm unaware of?

EDIT: And I think atticae's assumption is correct. As his behind-the-scenes video link confirms, that scene was shot in Sri Lanka, so someone probably asked the locals there how to say 'thank you' in their language and used that.