I know the basics of physics and magnitude of things well enough not to bother with that kind of effects. But of course I can estimate/calculate and at the same time show couple of different approaches for that kind of question:

1. Practical one: You have that 67m3 sized balloon which gives 2,2kg to 6,2kg of lift according the video. Values sound reasonable. Biggest of foil kites have ca. 4m3 of volume, so 1/17 of that. Theoretically we get 130g-360g lift for the 20m kite, and 45g-130g for a 10m kite.

These values would be possible of course for the black kite in sunny conditions, and if kite moves (like they usually do) airflow of course cools the surface. In reality perhaps 1/5th or 1/10th of added lift would remain, if even that. Then effect is few grams, for sure not more than a fraction of percent of the total mass of the foil kite.

There is also some air flow through the kite when it flies, which ruins the rest of "hot air balloon" hypothesis for foil kite.

2. Physical/mathematical one: You calculate how much air density decreases when temperature rises (pV=nRT, ρ=m/V etc.), or just find needed data. Then it is easy to calculate the resulting theoretical lift (after calculating the V of the kite.)

foilholio wrote:So I have been wondering about this for a while. It is obvious to me something is going on

Trust me, there is nothing going on with "hot balloon effect" and kites. That black solar balloon is however a nice work.