However i higly doubt that we won't survive to the death of our star. Even if it will grow up and will burn the Earth, we have 5 BILLIONS YEARS OF THECNOLOGICAL EVOLUTION to prepare ourselves to the problem.
200 years ago flying was considered impossible, 100 years ago was born the first aircraft, 60 years later we reached the moon, and now we reached all the planets and many moons and asteroids of our solar system (some of them with robots on their surfaces); we already discovered tens of extra solar planets with the characteristics to sustain life... I'm not worried at all.
The only problems, now, are the uncontrolled grough of the population (and so pollution, less food for everybody, ecc...) and the possibility of a nuclear war that could kill all of us... I'm quite worried about those