The overwhelming number of Thompson Center original 50 cal Hawken style rifles were offered in 1:48 twist, with a small number of "round ball barrel" rifles in 1:66. The examples of those that I've seen are so marked as such on the barrel.
The only plastic sabot I ever tried in my T/C barrels was the old "Poly-Patch" product briefly offered by Butler Creek. Being a shooter who likes "trying things", I bought some of those when I saw them, gave them a try and had poor results. I still have a bag of each design they offered, on my shelf. I have No idea how modern sabotted bullets will work in original T/C barrels. The inline rifles they are designed for have faster twist rates than your T/C. I have done some testing of my 1:48 barrel T/C Hawken style rifle using a variety of lead conical bullets without plastic sabot using relatively heavy powder charges in the 80-110 gn range with the goal of finding the best combination for hog hunting.
NOTE: I was not interested in comparing roundballs to conicals for this project. When I want to shoot roundballs from my T/C rifles, I use the Green Mountain barrels Dphariss mentioned with excellent results.
To evaluate conicals in 1:48 original T/C barrels I purchased and tested:
Hornady Great Plains conical. 385 gn HP/HB ( hollow point/hollow base)
T/C Maxi-Ball 370 gns
Buffalo Bullet Co. 385 HP/HB
T/C Maxi-Hunter 350 gn ( dimple-point...not really hollow)
T/C Maxi-Hunter 275 gn.
Minimum 5 shot groups, using various powder charges. All shots fired from a rest at 50 yds. with iron sights and my "old eyes".
Results:All of the conicals shot well enough to hunt with at the moderate ranges I typically encounter game in S.E. Georgia, 50 yds and less.
That said, the clear winner for precision (group size) was the Hornady Great Plains, 385 gn HP/HB bullet. Ragged one-hole groups at 50 with 90 gns of powder. With that result in the book, I bought several boxes of them, and went hunting.
The Hornady bullet performed flawlessly on Georgia hogs.