Beth,
As you may recall, I suggest the thermocouple apparatus to you some time ago, after trying it out in my own kitchen (I have one readily available to me). My set up was quite simple, a candle put inside a coffee cup, and the thermocouple held by hand, suspended in the air inside the cup.
I noticed very significant fluctuations in the temperature over time. Significant meaning fluctuations of +/- 10-20 degrees F over a few seconds. So it might read, in 2 second intervals: 130 134 142 130 128 120 145 165. (I just made that up).
There are a few reasons for that, I hypothesize. One, the thermocouple I have is very sensitive, as is normal for these devices. Second, hand holding adds variations. But most important, I suspect air currents play a large role. Burning a candle generates complex, perhaps even chaotic air patterns, because as the candle burns it burns oxygen, causing new air to be drawn in. And of course the high heat sets up convection currents.
The upshot is that I am not particularly surprised by your data, and don't trust it without knowing more. You gave readings once per minute. With my thermocouple set up, if I chose to, I could easily pick readings that showed an upward trend, a downward trend, or no change, just by varying when I took the reading by a few seconds. I'm not accusing you of cooking the results, but I'm sure you can see how unconscious bias might lead to the same result.
As others have suggested, you can already do a control trial. Do a burn for 20 minutes, and record the data. Shut down the system, and allow all temperatures to stabilize back to room temp. Do this several times, and you should start to see some patterns. If the data is consistant, then you are ready to try your test. If it isn't, then you need to find out why. Air currents? Differing candle height? Candle/wick variations? Soot buildup? Etc.
Once you have a reproducable control procedure which is very sensitive to changes in temperature, then you can proceed. Until then, I think you will end up chasing phantom effects when trying to control the candle with your mind. While what I wrote above may sound time consuming, it'll take a lot less time then running tests that aren't giving meaningful data, that may in fact give you misleading data (example: you may think you are moving the candle towards the flame, but you are really moving it away, but this is obscured by the error in the apparatus).
I'm sure you thought of a lot of this already, but I hope there was something in there that was helpful.