Hi.
I feel like you should make your decision on the Flop. With that kind of size, he's almost always shoving the Turn. So we have some options
1. Reshove Flop
2. Call Flop shove blank Turn while folding on a heart
3. Fold
Our equities actually don't really change much on Flop and Turn, assuming villain has a very wide value range comprising a good amount of non-flush hands and some semi bluffs
1) Flop equity (Optimistic)
Board: AhQhTh
Equity Win Tie
MP2 48.66% 47.13% 1.53% { AQs, ATs, KJs, Jh9h, Jh8h, 9h8h, 9h7h, 8h7h, 8h6h, 7h6h, 7h5h, 6h5h, AQo, ATo, KJo, AdKh, AsKh, AcKh, KhQd, KhQs, KhQc, KhTd, KhTs, KhTc }
MP3 51.34% 49.82% 1.53% { TsTc }
2) Turn equity (optimistic)
Board: AhQhTh5d
Equity Win Tie
MP2 50.67% 50.67% 0.00% { AQs, ATs, KJs, Jh9h, Jh8h, 9h8h, 9h7h, 8h7h, 8h6h, 7h6h, 7h5h, 6h5h, AQo, ATo, KJo, AdKh, AsKh, AcKh, KhQd, KhQs, KhQc, KhTd, KhTs, KhTc }
MP3 49.33% 49.33% 0.00% { TsTc }
3) Flop Equity (conservative)
Board: AhQhTh
Equity Win Tie
MP2 53.96% 52.36% 1.60% { AQs, KJs, Jh9h, Jh8h, 9h8h, 9h7h, 8h7h, 8h6h, 7h6h, 7h5h, 6h5h, AQo, KJo }
MP3 46.04% 44.43% 1.60% { TsTc }
4) Turn Equity (conservative)
Board: AhQhTh5d
Equity Win Tie
MP2 60.03% 60.03% 0.00% { AQs, KJs, Jh9h, Jh8h, 9h8h, 9h7h, 8h7h, 8h6h, 7h6h, 7h5h, 6h5h, AQo, KJo }
MP3 39.97% 39.97% 0.00% { TsTc }
I think it all boils down to your assumptions about villain's range. But assuming he has a wide value range here I think you can just play for stacks on the Flop immediately. Vs almost everything we have 33% equity at least, and sometimes he is bluffing with a heart, sometimes he is value raising 2 pairs and straights.