I connected a L7805 to a water fountain that I measured to be consuming 0.1 A at 5 V to regulate power coming in from three 5 W, 12 V solar panels connected in parallel.
The regulator is not heating up at all and is doing a great job, to my surprise. I calculated that it needs to dissipate 7 V · 0.1 A = 0.7 W.
How does the regulator do this without heating up? I thought linear regulators dissipated all excess energy? Is there something I'm missing?
12 V solar panels are a nominal 12 V, but may output more or less than 12 V depending on the load conditions and amount of sunlight. It sounds to me like your solar panels are outputting a lower voltage, which means the regulators are dissipating less power, so it stabilizes at a lower temperature, perhaps too cool to feel the difference from body temperature. It will be heating up at least a little, but it might not be possible to tell without a thermometer.
Your solar panels aren't delivering 12 V in your set-up, so the regulator doesn't have to drop 7 V.
Solar panels aren't voltage sources like bench supplies or batteries, they are more or less current sources over most of their V/I characteristics. This means that their voltage isn't always 12 V; their voltage is set by the input resistance of whatever they are connected to (V = I·R).
You can easily see this in action by first measuring the open voltage of the panels, without anything connected to them, and then connecting them and measuring their voltage again (before the regulator).
