I measured the weight of water to make sure it was the same every time.
I measured the weight of the canister before and after to get amount of fuel used. I made sure and wiped off any condensed water on outside of canister, but that was insignificant.
I measured the temperature before and after. I had a lid with a hole and a thermometer tip through hole. Little piece of wire around thermometer probe to keep it the same distance from the bottom – about half way between bottom and top of water, and half way between center and outside of pot. I waited a few seconds after turning off because the temperature rises a few more degrees. This should also equalize any differences between different places in the water volume.
I tried to do 180 degree F temperature difference from before to after, but each time was a few degrees different, but I normalized that out. I calculated the amount of fuel to raise 15 fluid ounces of water 180 degrees F. That's the amount required to fill up my thermos to make tea.
I've tried the strip of aluminum (works good), a copper wire (not big enough for enough heat transfer but a bigger wire would have woked but weighs more), and a container of water (works best, but more of a hassle).
I was thinking the water is best. I forget who it is that filled upside down canister with water, then put a lid on it, then turned it right side up, but I haven't found the right size lid. Because of this thread, I'm now thinking the aluminum strip might be better.
When I turned it down, it took 6 minutes to boil instead of the normal 3 minutes. This is with enough heat exchanger so it will run that hot. 6 minutes used 10% less fuel.
If you look at a shadow in sunlight you can see what's going on. With 3 minutes boil time, the hot gasses go all over. With 6 minutes, they stay closer to the pot.
It's all basic chemistry or physics or whatever – the butane gives off so much heat when it combusts, and then some of the heat blows away into the air. It doesn't matter what temperature it's at. At least to first order.
Yeah, if it's colder, there will be a little more radiative heat loss, but I don't think that's significant.
Numbers are what I remember off top of head, but there was a 10% reduction in amount of fuel used when I doubled boil time.
Also, if you only heat up to 190 F or so, where it starts making hissing noise, and then let it sit for 1 minute (or several) it will kill any bugs and save another 10%. (Since none of this is necesary and you can drink untreated water just fine, you could just not heat it up at all and save 100%, except that doesn't make for good tea or oatmeal – just kidding).