John, first off, a caveat - though I have made and continue to make yogurt many times, I am no expert, so take my thoughts with a grain of salt!
I did a little digging into the two bacteria you found on the label. "Bifobacterium" apparently covers a whole range of species. But I didn't see whether they were mesophilic or thermophilic or something else. They are active in the human gut, so presumably they thrive at 37°. The L. casei is apparently one of the primary non-ripening LBA -- i.e., bacteria naturally found in milk that add flavor, but don't lower the pH significantly -- and I'm inclined to think it is probably a mesophilic, though Wikipedia says it tolerates a wide range of temperature and pH.
As we discussed, my assumption is that the ramp-up from lower temperature will encourage / allow mesophilic bacteria to develop before they begin to deactivate and perhaps to die at the upper temperatures. (As I recall, most meso bacteria die somewhere in the range of 41-44° - so the upper end of your temperature range might or might not kill them off, but at the very least should keep them relatively inactive.) But they will stay active all the way up to at least 37-38°.
So your proposed temperature profile will keep the milk at low and meso temperatures for 6-8 hours. Since the casei doesn't ripen the milk, and I'm presuming the bifidus doesn't either, presumably this just lets a whole lot of them develop for probiotic properties; then the thermophilic strains begin to kick in and ripen the milk, eventually leading to its coagulation into yogurt. I don't recall when thermo bacteria begin to become active; I'm guessing it's around 30°. If that is correct, then the thermos will start working after about 3 hours into your temperature profile, and gradually will become dominant after maybe around 8 hours.
Please note that there is a lot of guesswork and assumption in my "analysis" above, so again, take it for what it is worth. But if I'm vaguely correct in my guesses and assumptions, I would think the profile you suggest would make sense. The only quibble of concern I would have would be whether the time at low/meso temps could allow any unwanted contaminants to get a foothold - so use good sanitation, as always, along with a lid.
One other thought - are you going to heat the milk to 82-83° first? Not only would this help to eliminate any unwanted bacteria in the milk, but it also helps to denature some of the proteins that otherwise stay in the whey. This will give a thicker, richer final product. I heat my milk to 82-83° (180° for us Fahrenheit types) and hold it there for 30 minutes, stirring throughout; then I cool it rapidly in a sink of cold water down to the target temp - which for the yogurt I make is 46° (115°F). Since I've been doing this, it has made a really significant difference in the thickness/texture of the yogurt. Using whole milk and/or adding some additional cream sends it over the top into gastronomic delights.
Of course, the most important thing of all - try it, and give us the report!