We-e-e-ell . . .
The velocity in the growth of technology increases exponentially. It is very possible we may reach a level of understanding to, within this century, learn to moderate the output of our own sun. This being the case, Hawking is, shall we say, spot on.
Then again, perhaps some other space-faring lifeform will beat us to the cataclysmic punch...
It's a pretty big Universe.