Over all the sun IS burning out. That does not mean the sun gives a decrease in energy directed at earth. The sun changes. There are explosions on the surface that change all the time at any given projection of energy. So the point about the sun overall "cooling", has nothing to do with what is happening on the suns surface that directly projects toward earth.
Your statement that "the sun can't be the main control of the temperature." does not make any sense. The sun is absolutely the main control since it is the source of heat/energy.
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