The hand is certainly strong enough for a raise IMO.

I don't think the turn is an insta-fold either. Unless the Villian has K-J-9-x with 2 hearts (and not the K as one of those hearts), you have ~33 equity.

Thus, you are correctly priced in for a call on the turn and can check/fold if you don't hit a 4, 8, 10, Q or non-heart K.

Calling the turn may also allow you to a cheap showdown if your opponent decides to check the river.