Straight on the flop

On the turn you have 88% equity:

Board: K♣T♥Q♣ 3♥
       Equity     Win     Tie
BU     88.79%  83.17%   5.62% { AsJc }
SB     11.21%   5.59%   5.62% { 88+, A8s+, KQs, QhJh, JhTh, Th9h, 9h8h, ATo+, KTo+, QTo+, JTo }

Even with the heart on the river you're still ahead of the range I gave the opponent.

Board: K♣T♥Q♣ 3♥ A♥
       Equity     Win     Tie
BU     82.47%  68.04%  14.43% { AsJc }
SB     17.53%   3.09%  14.43% { 88+, A8s+, KQs, QhJh, JhTh, Th9h, 9h8h, ATo+, KTo+, QTo+, JTo }

The big variable is: What is SB's range in this hand?
 He has to call a 4BB raise out of position
 He has to call a 1//2 pot bet on the flop, and a 3/4 pot bet on the turn.

I messed around a bunch and give opponent a very heart-heavy range and you're still ahead.

Board: K♣T♥Q♣ 3♥ A♥
       Equity     Win     Tie
BU     83.33%  78.79%   4.55% { AsJc }
SB     16.67%  12.12%   4.55% { TT+, AhKh, AhQh, KhQh, AhJh, KhJh, QhJh, AhTh, KhTh, QhTh, JhTh, Ah9h, Th9h, Ah8h, 9h8h, AQo+, KQo }

Still, if you gut says "fold" then fold without a backward glance.

I'd bet bigger OTF, maybe 75%+, vs this lineup of whales, expecting to get called by all the pair+OESD's, FD's, two pair, etc. If we get more than one call we can maybe even shove OTT which would be awesome. I would fold the river also. Most? fish will not shove the river with a straight here, given the possible flush.

Good fold...

Very wet flop -> bet bigger OTF. I would go even for pot-sized. Shove turn. River is marginal... I would have probably called, but I am sure that the most you can get is split.