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But the electricity will be used to power all sorts of appliances, most of which generate heat. So I don't think there will be a noticeable difference on a planetary scale unless you use most of the electricity to ship energy out to space. If there is any change to the global temperature, it will probably be due to the albedo change (amount of sunlight that gets reflected off all those shiny panels of glass).

You could always use that excess electricity to run energy-intensive processes to store the power chemically. For example, split water.

No, since electricity is just another form of energy that will sooner or later be turned into heat. You'd have to remove the energy or store it to regulate the temperature, so either mirrors or any form of long-term energy storage would work.

Or turning it into chemical bonds like plants do? It reminds me of Buckminster Fuller describing fire as "sunlight unwinding from tree trunks". Or burning oil as unwinding sunlight from lots of prehistoric plants and animals.