Yes in about 4 billion years the sun will be gone but we will be gone well before that burned to a crisp as the sun will expand and gobble up Mercury and Venus.
You seem to get confused easily - I never mentioned anything about the Sun burning out so what follows after your comments makes no sense.
This is the sentence that makes sense "If the sun's energy is decreasing while the Earth is warming, then the sun can't be the main control of the temperature." Read the whole sentence and do try to understand.