Some people, incorrectly in my opinion, use the requirements of their house in their figuring of burn time. To me, burn time in a BK is active cat time, and burning two of them for 3.5 years, I’ve not noticed any dependency between outside weather and burn time, for a given thermostat setting.
If you use, “I need to load it every xx hours to keep my house warm”, or “I turn it up when it gets cold,” then of course weather effects your burn time, but that’s a different conversation.
One thing I can imagine is that if one runs an OAK, the variation in outdoor temperature would affect the the temperature of the thermostat, accordingly. In this scenario, a colder OAK supply would cause the thermostat to open the air more for the same t’stat setting, and this decrease burn time for a given knob position. It seems feasible, but I have no experience with OAKs on BKs.