I'd put him on Ax, Khx (maybe something like K9+), and all PP's preflop. On the flop, you can rule out all PP's TT and under, and most likely JJ+ that doesn't have the heart. Khx is very like at this point, maybe something like KQ. If he's doing this with AA he's a total donk. So yeah, Ax (even moreso with a mid-high heart), Khx and JJ+ with a heart.

I originally voted to bet the flop and turn, but given his stack size I just shove. No sense in letting him see another card for a flop bet of $4 that will commit him in the hand anyway.

And yeah there's a small chance that he flopped the flush, but even still I'm still shoving w/ the redraw to the boat.