Definitely going to the river here. The dead ten makes trips less likely. There's nothing wrong with getting as much in the pot as possible on fourth. You are roughly even money against any pair in the hole, and if a third player wants to come along that's fine. If my hearts were more live and stronger, I would three-bet fourth.

Also, it is not correct to say that it is OK if this is checked through. Assuming villain does not have trips, you have almost 50% equity in a three or four way pot. Missing the opportunity to get money in is not good. Check-raising the guy who re-raised third is a possible line here.