[CalRobert]

Right, but energy that would have heated the roof goes towards powering the aircon (which likely is on the roof itself), which then emits the same amount of heat, no?

Say a roof is absorbing 10000 watts. You install solar panels that absorb 2000 watts, used to power an airco. You now have your roof absorbing 8000 watts (released as heat) and ann airco absorbing (using) 2000 watts (also released as heat). Am I wrong? Seems like a conservation of energy problem. And you get a cooler roof so less airco demand too!

[CalRobert]

Ah, unless you refer to shifting the release of heat from inside to outside earlier in the day?

[grey-area]

No the solar panels do not absorb only infrared or even mostly infrared.

[CalRobert]

OK, but I don't see how that addresses what I was getting at?

As a thought experiment, imagine you attach a heater to the solar panels (maybe it's a sunny day in winter). Do you get free energy for heat?

[grey-area]

Nobody said there was free energy, but heat is not the only energy available. Here if you like in your analogy visible light is turned to outside heat and inside cool. But it’s simpler just to think about the heat inside the house - heat is being transferred from inside to outside.