BK exhaust temperatures can run very low at the lowest burn rates. All modern high-efficiency stoves share this challenge, putting less heat up the flue is precisely how they achieve that high efficiency. However, with it's super-long burn capabilities, BK really pushes the envelope, in this regard.
Your tall pipe might cause control problems with many stoves, but not a BK, I'm actually running one on roughly 30 feet of pipe myself. No issue with control, even without a pipe damper. But, you may have two other issues:
1. If it's a clay liner all the way to the top, rather than an insulated steel liner, you may have trouble with the exhaust cooling TOO much, on its way to the top. This can increase creosote deposition. Not a huge problem, but it might lead you to sweep every 2-3 cords, instead of every 4-6 cords. This will likely be more an issue if you run it low and slow, than at more moderate burn rates.
2. A very strong draft can cause stirring of fly ash, which can get drawn into the combustor. This isn't much of a problem on the Princess, there have been more of these issues reported on the BK 30 models, and I can only think of one Princess owner (ever) mentioning this issue, here. In either case, it's easily resolved with a key damper, which I run on my BK 30.
If you're wondering why my item 1 is implying low draft, and my item 2 implies too-high draft, just remember that your draft will vary with flue temperature and air inlet control (restriction)... among other factors.