Heat death doesn't mean that there is any less energy than today. It simply means that the energy is all disorganized (entropy) and cannot be used to do any useful work.
Basically we would have to break the second law of thermodynamics. But why worry about that now? We don't have any where to go when the sun dies so it really doesn't matter.
Good point but what's to say another star of greater proportions won't take its place? Heck this is still so far away that your great, great, great, great grand children might witness this and by then there could be two suns. Check star patterns and the possibility is more likely then not. What is your theory? Another possible ice age? I think this is just more hum drum what if BS show your theory or any kind of solid facts. I hate the chicken running around going the sky is falling! SORRY!
I don't think you guys are grasping the time scales here. Ice ages happen on the order of every 100,000 years. The sun will live about another 5,000,000,000 years. That's not 7 generations of your offspring, but 160,000,000. Heat death is on the order of 10^100 years.
And no, another star won't replace our sun. They don't just appear out of nowhere.
Also for another star to reform out of the remains of a supernova would take so long that everything on Earth would have died any way. Also we do notknow how much matter (dark matter etc) is in the universe so we don't know if it will expand for ever.