ATs in 3-way pot

In a session I played yesterday, I believe, I had this hand come up. I think I played it well, but not necessarily optimally. So I'm soliciting opinions.

Here's what we know about the opponents. Nothing. Yeah, you got it. Nada. The game is 25c/50c LHE RUSH on FT. I have no HUD running and no notes on either player. Take a gander and tell me what you think.

Full Tilt, $0.25/$0.50 Limit Hold'em Cash, 6 Players

Poker Tools by CardRunners - Hand Details

Preflop: Hero is CO with T A
UTG folds, MP raises, Hero 3-bets, BTN caps, 2 folds, MP calls, Hero calls

Flop: (13.4 SB) T 6 7 (3 players)
MP bets, Hero raises, BTN 3-bets, MP calls, Hero calls

Turn: (11.2 BB) A (3 players)
MP bets, Hero calls, BTN raises, MP calls, Hero calls

River: (17.2 BB) K (3 players)
MP checks, Hero checks, BTN bets, MP calls, Hero calls


Here's my reasoning behind my play. I'm 3-betting preflop to knock out the button and the blinds and take it heads up. The button caps and we go to the flop 3-ways. Having no history with either player I'm not trying to nail down a read yet, but generally putting MP on big cards and BTN on AQ+ and pairs.

Flop is great for me, so naturally I raise only to get 3-bet by the BTN. When the MP calls, I'm putting him on a JT/QT type hand, possibly with backdoor straight/flush draws. Button's range hasn't changed. Inclined to believe he has a pair, but not necessarily beating me. Not a disaster but proceeding cautiously. Trouble card on the turn. A. Now I either have the best hand or a 4-outer. It's not exactly a WA/WB situation, because my opponents could have up to 12 outs each. In this case, I've decided to just call down.

Okay, you know my side of things. Tell me what you would have done.

M