The pot has to handle the full output current, but only has max 1v2 across the element. You probably will want to use a 5W wirewound unit, as to get the full current of the 317 you will pass just short of 2A through the pot and this will be in a small portion of the range, so you need a pretty high power dissipation to handle this. You need a pot that can handle 2A through the wiper, which means at least a 5W wirewound unit.
The LM317 does dissipate most of the power though, so you will need a heatsink that can handle the dissipation of the unregulated supply voltage multiplied by 2A into it, or you need to have a preregulator to dissipate most of the power instead of the regulator. With this then you typically have 5-8v across the regulator chip.
Thanks for the reply @SeanB.
That seems like a pretty ugly application... Do you think an OpAmp mosfet current regulator is a better choice?
How would I put that in the circuit? Just tack it on the input side of the voltage regulator circuit?
I'll look up some example circuits but from what I understand it would be a reverse process - so when the current reaches the set point it opens the mosfet to ground? Would the mosfet connect to the adjust pin of the lm317? Still trying to figure out how that works on paper.
I'll be able to actually see what's going on when Mr. Lorton's old scope arrives!! (Thanks again Martin!!!) which should help a ton.
From Mr. Jone's EEVBlog it sounds like it will oscillate in current limit mode, which makes sense. He uses it with another chip so I'm not sure that same application will work with the circuit I have at the moment.
So many things to learn and test.
Cheers