Not to worry, however, because life on Earth will end much sooner than that, when our sun enters the red-giant stage of it's life, it's diameter will reach Earth (having engulfed Mercury and Venus). In all honesty life would probably end before this phase. The sun will become a red giant star in approximately five billion years (about when our galaxy starts getting consumed by Andromeda). However Earth will have gotten too hot for life to continue a bit earlier than five billion years from now.
More heat means more water vapor and less carbon dioxide, so the plants will go first. As plant species go extinct, the animals will decline too pretty much simultaneously. In approximately 2.8 billion years scientists estimate that only the hardiest of microbes will be left behind. Once temperatures reach over 140 degrees Celsius, DNA breaks down, and even those microbes will be lost.
Image courtesy SDO/NASA
Don't fret, however. This is an unimaginably long time away.
Or, perhaps, fret a lot, because current rates of climate change weren't given a lot of consideration, and that's looking bleaker by the second.
Sources.
Milky Way Will Be Consumed
Biosignature Doomsday