Answers:
Why would I expect this? (linear function of temperature rise), while the formula I provided is clearly non-linear; within the observed temperature changes which are typically under 30 C per cycle, the formula deviation from linear is almost nil. Run it through a spreadsheet to see what I mean. A linear fit R squared hangs around .95 and doesn't deviate much from the formula within those bounds. Clearly over a wide range of say 600 C it's obviously not linear. Point being, with the only data set I have access to, I would expect a linear behavior within the observed temperature ranges using the provided (non-linear) formula (more below per your critique of choice of formula).
Re the turbulence issue, we'd need a Navier-Stokes simulator to get a handle on how significant turbulence is, which I don't have. I don't discount it, I just have no means of simulating it. I don't think either of us actually knows if there is a vortex shedding from the magnetron. Absent a simulation or a nice schlieren photo, neither of us really knows what's happening. Perhaps we both suspect thermal effects, but the DIY community needs a bit more than an assertion that "It's all thermal". I know the burden of proof is on the DIY folks to prove it's NOT thermal, but as you point out this is a complex fluid dynamics problem and providing guidance would help them narrow the options. I'm out of my pay grade to provide this to them. Perhaps it's in your pay grade? :)
As to why the choice of formula, I was pointing out that the basic formula for a hot-air balloon lift calculation is insufficient, which I think you pointed out with your first question. In this context, I was proposing that an argument that these effects are thermal, albeit plausible, cannot be simply stated as a conclusion. I'd like to see a simulation or a calculation that matches the observed data from a purely thermal point of view. My "lift" formula doesn't match the data. It's obviously wrong. What I don't know is what an appropriate formula/simulation would look like.
As for the algorithm used and the statistics used see this post: http://forum.nasaspaceflight.com/index.php?topic=38203.msg1430941#msg1430941
The VBA used is further down the page from that link. Basically, it stripped out the on/off cycles into groups that could be treated for slope analysis.
To this point I've had zero critique so if you'd care to shred my approach and analysis, go for it. :)