My noobie 2cents...

1. I don't play JT in EP
2. Think about why you would play this hand. You've only got a couple of basic options that are favorable for you. Hit top pair, two pair or some kind of draw. If you're playing deep (80BB+), you're prolly not going to be happy stacking off w/ TP T kicker even if you hit -- so you'll prolly want to keep the pot small.
3. Stack sizes are a big deal here. JT as a draw will play nice multi-way against deep stacks giving you great implied odds. Deep stacks will suck for most J top-pair hands. Heads up against a loose shortie with an SPR of 3-4 and you may be okay committing with top pair. Deep stacks, I'd stick to playing this for draw / two-pair only.
4. I'm not cold-calling a PFR with JT (usually...) There are exceptions, but since you didn't say this is suited. I'm prolly folding JTo to any real aggression PF. The pot will be too big to make playing top-pair viable, and I'm going to have to prolly commit a big chunk of my stack to play a draw unless I flop really goot.

so.... if you made it through those ramblings (and that's only some of the stuff you want to think through...)

3T8 flop - You're behind QQ,JJ, dominated by AT,KT,QT, possible staring down a suited one-gapper that's already got an open ended, and way behind 33,88 and TT. You're ahead of a bunch of random paint that might have called a raise (AK,AQ,AJ,KQ,KJ). How much of your stack do you really want to commit with this top pair? If you raised, are IP and the odds are good they'll fold to a c-bet, then I'd fire one... otherwise, I'm looking to keep this pot small.

AT4 flop - Pretty much same as above, except now you're squashed by any Ax hand. I'm checking this IP and prolly check/folding OOP (unless it's something stupid like a min-bet... then I'll see another street)

2J9 flop - I think this is your best flop. 8 outs to an OESD, less chance of JJ out there and you're beating TT, plus back to top pair. Same as #1, but I might be more inclined to check/call OOP.

I guess two main things for me on this... 1) small hands and un-made draws like small pots with big implieds -- I'd keep the pot as small as I could until I hit something better than one-pair 2) stack sizes (yours and opponents) and having a related plan is critical to all your pre-flop action, including whether you'd even consider playing this sh!t in the first place.

Hope I didn't confuse this sh!t too much... Think I'm gonna go back to confusing myself now