Grimm - autos in general don't like heat. You can wreck a THM400 or an A727 in short order by overheating it. I've even seen Powerglides get wrecked by overheating!
To identify the manual transmission, slide underneath and look at the case. The BA/10-5 uses a "clamshell" case, and there will be a longwise parting line down the length of the case at the bottom. The AX-15 uses a "centre plate" case, with the main loading done on a heavy plate, and the front and rear case sections bolted on afterwards.
(In this image, the BA-10 is on the right and the AX-15 is on the left. If you look down almost the right side of the BA-10 case as pictured, you'll see where the case splits for loading. Both units still have the transfer case attached.)
The BA-10 is rubbish - I've wrecked
four of them with merely normal driving (it was designed for, probably, the Peugeot 505. It has half the engine, a third the power, and has a kerb weight about eight hundred pounds less than the XJ. Also, the gears are made
too hard in the BA-10 - about HRC65 or so - and that's why the teeth end up stripping off of them.) The AX-15 is a favourable transmission, and I'd feel confident towing with it - although I do think there are better options as well (like the NV3550: 2000-2001XJ, 1999-up TJ.) The BA-10 is barely fit for scrap metal in the first place, and it should be serviced (by replacing with an AX-15 or NV3550) at your first opportunity. Besides, getting a new transmission mount cushion borders on prohibitive for the thing...
The
only good thing I've found about the BA-10 is that it was easy for me to get replacements - just ask for them and go pick them up. People are probably still getting rid of them left and right. I had to actually swap something for one of the AX-15s I have (the external version,) and we both came out ahead on that one. It will be going in as part of the refit on my 88.