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First, it sounds like you're calling T16000 into a pot of T31000. That means you're getting nearly 2:1 to call.

Assuming your opponent is not on a pure bluff, what are some made and semibluff hands he can have? And how often will you win?

AhKh: 35%
AhTc: 70%
TcTs: 4%
AhAc: 65%
KhKc: 65%

In other words, you're getting the right odds to make this call. If your villain has TT, that's the breaks. If he has the made flush, that's exceptionally painful, but you DO have odds to call, so if you lose, that's harsh. But if you win you're in *great* position to be way up in the money.

I personally think a naked high heart - possibly as part of a pp - is the most likely holding here, because I think the made flush smooth calls you and I think the non-heart hand leads the betting since he was the pfr.

So yeah, I call.