I know it is all words ... gotta admit, that's what you two have been doing.
It would appear that nobody has actually done this sort of testing definitively and, considering I've been gearing up to do this sort of tests on the solar cabin where our hives are going in, I guess I must be the guy who gets to do it. Frankly, I'm amazed that this has not been done. And given my personality, there is no way I'll go to this effort without sharing.
And after posting my ideas, I read Mr. Bush's. I think he's pretty much got it, just somebody needs to prove it.
I would be willing to bet that nobody else here has the head start on equipment ($2700 data acquisition system, $2000 thermal imager, career in instrumentation and testing, and newly-discovered way to make $5 heat flow sensors instead of $280 heat flow sensors). A few have hive scales, but not too many outside of universities can log weight continuously.
Indulge me. I won't have bees until mid April, and then I won't have winter until next winter.
The easiest way to debunk the idea that it is solar gain will be fairly simple. Peltier effect cooling devices are thermopiles, and will generate voltage proportional to heat flow. I've calibrated a handful, but they don't even need calibration to prove or disprove this point. Just stick them on the hive roof and sides. If more heat is going out than in, averaged over a cold sunny day and night, well, there's that possibility gone.