I understand that the solar sunroof only operates when the vehicle is parked with the engine off.

Is there any thermostatic control associated with the circulating fans, or do they run as long as the sun shines?

Is there any interconnection with the A8's electrical buss? Does the solar sunroof supply any charging current to the vehicle's battery?

A trickle charge function would be a nice feature, my S6's battery will rundown in about 3 weeks without use.

run as long as the sun shines. Don't know if charges the battery, I dont' think so.

The solar sunroof is a GREAT feature. I wouldn't have chosen this option if i'd ordered the car myself, now i can't imagine ordering a car without this feature. It does not charge the battery, it is it's own self contained unit running the fans only (does not run the AC). I cannot find a reference as to a thermostat, but it seems it has some temperature control. I was able to hear the fan running when i entered the car on hot summer days, but as the weater is cooler, it does not seem to run. It is possible to turn the feature off via the MMI, for when parked in a dusty area etc. It really helps to the interior from baking on hot summer days and allow for quicker cool down with the AC.