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That makes me wonder if the installation of solar panels on a roof act as "shade" similar to partial tree coverage in some way, since in many cases they add a thin cushion of shaded air between the panel and the roof. I wonder if that provides any meaningful shade or temperature reduction.

Not making an argument either way, I just hadn't really considered if this was a factor until I read your comment.

It does. Not in Texas but Australia and one of he rooms that got solar became slightly cooler after it was installed on those very hot days.

The shade from the panels does make a big difference in summer, according to a friend of mine in Colorado who has had panels for many years now.

I would certainly never cut a tree down to get more solar on my roof, even if the math worked out favorably from a cost perspective it just feels gross.

Awnings are a cheaper alternative which can block direct sun into windows, making a huge difference in room temp.