Yup. In approximately five billion years or so, when Sol runs out of hydrogen in its core, it will start to fuse helium instead, and it will rapidly run out of elements to fuse until it reaches iron. As part of this chain reaction, it will drastically swell in size, easily engulfing the four inner planets of our solar system. Earth will be consumed in a ball of flaming gas and plasma. Of course, by this time the oceans will have entirely evaporated and most lifeforms will be extinct, including humans (unless we manage to somehow become a spacefaring species), so it's a moot point.
The real problem is how, if humanity is to endure billion-year epochs, our descendents can avoid the heat death and collapse of the entire universe. THAT will be FAR harder to deal with than the destruction of Earth. But I'll leave the problem to them if they make it that far. Unless, of course, we develop a feasible avenue to immortality within my lifetime, at which point I'll see if I can wait it out with them without becoming bored/insane and committing suicide as a result.