Well... I do wanna argue a little bit haha surprise surprise
ok.... Let's say your water is 170, it needs to raise to 180 to kick off.
Your draft has just opened, how does the firewood/fuel your burning know what the temperature of the water is around it?
Now from my experience one thing that I have seen make a hotter burn because of the amount of time it ran was having a bigger swing in temperature. Let's say if you have a 5 degree swing and it takes ur stove 8 minutes to recover, let's now say you have a 20 degree swing and it takes ur stove 25 minutes to recover, the longer burn from what I've seen can actually have higher firebox temps and burn off more creosote.
I have stood outside with a temp gun on the door of my stove comparing how different intervals change the temp, and longer runs equal hotter temps on the box. Now as far as your water temperature causing an increase in fire temp, I don't get that.
A btu is a btu, it's the amount of energy it takes to raise a pound of water 1 degree