I also assume that by a heart draw you mean only 2 hearts out.
I actually think it could go the other way here kennyg, why would an overpair bet $4 into a $13 pot on such a dangerous looking flop? Wouldn't a $10 bet be more appropriate there? I think his underbet looks more like an A-K or A-Q that missed but he's read hellmuth instead of TJ and wants to lead out anyways. I was going to say that raising the turn might be a good play, but I liked your point about being more likely to take his stack if he has an overpair. I think the only hand you are really in trouble against here is A[h]K[h] or A[h]Q[h] so smooth calling is probably a relatively safe play.

If Im playing at Party with the short stacks, Im going all in.
After the $10 turn bet there is $50 in the pot. The guy only has $22 left. Hes not seeing the river without paying for it if hes playing me.
I think hes going to check/fold the river unless he hits something (flush maybe).
You thinks hes going to bet again with 4 cards to a str8 on the board if he doesnt have it? I dont, but he might call a raise praying for a flush if thats what hes looking for.
If he has the flush draw, and you go all in, it'll be $22 to him with a pot of $82. He'll be getting odds to draw so I doubt he'll fold.

Well seeing as I'm trying to work off a $150 deposit bonus on PP right now I'll keep that in mind (playing the $100 max tables)

I didn't read all of the responses but I think it's obvious that you need to raise here. Depending on how big his stack is, you can raise 2/3rd of his stack, effectively committing him but not making the raise look too big, or you can just put him allin if he has significantly less than the pot. You raised him on the flop and he is leading into you again, it's pretty clear that he is gonna call a raise. He may have a Jack too anyway, but I can't imagine him having QJ so get the money in on the turn where you are guaranteed at least a split.