Time for a super-thin river bet?

Full Tilt Pot-Limit Hold'em, $0.10 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP1 ($4.85)
MP2 ($12.95)
MP3 ($5.95)
CO ($3.20)
Button ($4.55)
SB ($26.70)
UTG ($10)
Hero (UTG+1) ($14)

Preflop: Hero is UTG+1 with J, J
Hero raises to $0.35, 2 folds, MP3 calls $0.35, 1 fold, Button calls $0.35, 2 folds

Flop: ($1.20) K, 3, 10 (4 players)
Hero checks, MP3 checks, Button checks

Turn: ($1.20) A (4 players)
Hero checks, MP3 checks, Button checks

River: ($1.20) 4 (4 players)
Hero checks, MP3 checks, Button checks

Total pot: $1.20 | Rake: $0.10
Well, we could hope for a hero call

[yourfather]

I bet the flop and don't bet the river.

[d0zer]

If villains are bad enough that they'll call anything you beat on that river (after the flush comes in), then you should be betting the flop to get value from like JT/draws.