The idea that ten billion humans are going to take off in spaceships and abandon the Earth is utterly preposterous. The last human on Earth will die on Earth, not leave it for some other place.
I wonder how these thousand years might look if currently there have been temperature difference of extremes by 20 degrees, with average already raised by 2.
For example, mass extinction of oceanic ecosystems is due to somewhere around 2050s. Whole oceans will get empty very quickly. http://science.sciencemag.org/content/314/5800/787
Collateral victim count of ~3 trillion yearly deaths of oceanic animals is a big contributor.
We'll see how the world will cope when main oxygen producers disappear.
Otherwise we'd all be like "good, in a thousand years everything's going to be ok, 'cos science".