A BTU (British thermal unit) is a unit of measure that relates to the quantity of heat required to raise the temperature of on e pound of water one degree Fahrenheit.
My opinion / hypothesis and why is…
The lower the beginning water temperature the more BTUs will be required to bring the quantity of water to a boil.
The ambient air temperature can steal away some of the heat from the water container (cook pot) if it is cool to cold. If the ambient air is relatively warm to hot it may have little or no effect.
IMHO the amount of fuel is directly proportional to the amount of BTUs available from a given stove and the fuel used in that stove.
As the amount of water to be boiled is increased the amount of BTUs needed to bring it to a boil increases.
More water requires more heat (BTUs). More heat can come from a larger stove and / or a hotter burning fuel. Less water equals a smaller amount of BTUs needed for a boil which could relate to a smaller stove and / or a cooler burning fuel.
IME on my last 24 hour overnight I needed more fuel to achieve a boil with approximately 50 degree water in ambient temperatures that were about the same than I did using my same stove in my tests at home using 75 degree average temperature water in 80+ ambient temperatures. I've discounted the effects of wind for the simple reason that my tests were done in calm conditions and on my recent hike supper was prepared in dead calm conditions.
Dan you took me all the way back to school and my text books! ;-)
Party On,
Newton