Yes, as it gets colder draft will improve, and you will be able to maintain lower settings without stalling the cat.
I'm not sure what you call medium, and you don't even state which stove you are burning (BK has many models), or if your newly-installed stove is even new or used. You also don't state what type of wood you are burning, or it's condition, so any answer here is going to be pretty ambiguous. I can get consistent 30+ hour burn times on an Ashford 30 on 15 feet of chimney, meaning the cat is in the active region of the thermometer for 30 hours, when burning nice dry red oak in temperatures consistently < 40F. If the temperature climbs much above 40F then I cannot turn the stove down far enough to hit 30+ hours on that short chimney, and if I burn anything less than oak I also can't quite hit those numbers as the wood disappears faster. But I would have to burn at a pretty high rate (like above 4 o'clock on the Ashford 30 dial, I suspect) to consume a full load of oak in 7 hours.
Those who burn pine, or other wood that I wouldn't bother using, will see shorter burn times. But I suspect even then they'd be able to do at least double the burn time you are seeing.
I wouldn't assume this is an install problem, so I'd not jump to call them back right away, until we can get a better idea of what is happening. Here' a start:
1. What model stove, and is it new or used?
2. What species wood are you burning?
3. How long has your wood been split and stacked, and under what conditions?
4. Describe your chimney setup, height, diameter, pipe type, cap, elbows, etc.
5. Describe your operating procedures.