It is basically never correct to limp into the pot, unless other players have limped already, and/or its a game with antes. This was a cash game without antes, and then you should always raise or fold, when nobody has entered the pot ahead of you.
This is a pretty fundamental thing, so I am a little surpriced, two forum members tell you, that limping is correct here. 6-max NLH is solved to such an extend now, that this is not really up for debate, and everyone can find the answer by reading strategy articles etc.
If you are the aggressor preflop, then Villain probably check to you on the flop, and on this board I would check back and take a free turn card. At least this gives you one more shot of making your set or perhaps picking up a straightdraw.
As played I would also fold on the flop. Sticking around with third pair and no draw just get you into sticky situations, where you have no idea, whats going on, and basically you are just hoping, the guy is on an airball bluff.