Kamelryttarn, that is an impressive array of instrumentation. Thanks for taking the time to dig into the system and share the results. I wish I was smart enough to understand all this electrical stuff. Myself, I don't trust electrons. They're sneaky little devils. I mean, like, have you ever seen an electron?

I guess its good to have a handle on current and wattage and voltage, and just what those values are doing under varying operating conditions, but it seems to me that the original question centered around elevated temperature resulting from the regulator dumping more energy.
My bike is currently engineless. If it was operational, I would do a simple test to determine if the regulator ran hotter when the headlight was disconnected.
Start the test with the regulator at ambient temperature. Take the three 6mm bolts out of the seat, put the seat in place, and go for a ride of predetermined length & speed & time. Pop the seat off and shoot the regulator with an IR thermometer.
Let it cool down until the regulator is back at ambient. Disconnect the headlight. Then repeat the test ride (same length, speed, time). Pop the seat off and shoot the regulator with the same IR thermometer.
Did it run hotter, the same, or cooler?
Of course, if it runs hotter with the light disconnected, we will be faced with the question "how hot is too hot?".