Yes. I had some data that proved this, but it was lost with the rest a few years ago with the hard drive. Anyway, as I recall, there was like a 15 second differential for two cups of water boiled to 200F from 40F. This was over the couse of like ten or twelve burns as I remember. It drove me a bit crazy because everything was "supposed" to be equal...pot, cone, water temp, etc. I was doing the same as Franco and simply snuffing it out when I got done with each test run, though. Then adding an ounce of fuel. It did bias the results as the stove filled more and more. I tossed those results and simply let it burn out each time and ignored it.
The reason? Well, not real sure, but I suspect you are correct about the fuel cooling the stove. More specifically, the chimney area. The differential heating between the top and bottom (as well as the actual combustion) causes air to be sucked into the flame. If it has more differential, this is roughly the same as making a longer chimney column, it means slightly more air, hence more combustion or a hotter flame. Again, I have not really looked at this specifically, since I simply built a taller chimney stove with more air inlets (yes, it does burn hotter though it has a smaller heat outlet.)