But, as the mantle continues to cool, the crust will eventually stop moving (though a few magma pipes will still reach the surface, similar to the end times on mars that led to artifacts like olympus mons), water will become permanently trapped beneath a surface that becomes ever more dry and cold, sporting a thinner and thinner atmosphere that has dwindling amounts of water vapor and carbon dioxide (both of which are greenhouse gases.) As these processes kill off life [as we know it], plants will no longer be able to produce oxygen (at least in useful quantities), thus further thinning the atmosphere (and the thinner it gets the colder). That, and what oxygen remains will rabidly bond (oxidize) with the soil, disappearing largely forever.
In other words, Earth is already heading down the path to become another, fatter, Mars. By the time it reaches this status, Earth won't be very much warmer than Mars is now, regardless of its distance from the sun.
Internal heat + External Heat + Atmospheric Recycling (geogenic and biogenic) + Magnetosphere to protect the atmosphere... we can't live here if any one of these disappears.
Conversely, there are places in this solar system that may be good habitats right up till the sun sheds its skin... i.e., beneath the surfaces of 3 out of 4 gallilean moons. Due to kneading by the gravity of Jupiter, their cores will remain hot for far longer than Earth will with the assistance of the ever-distancing Moon. Being beneath the surface would also help shield settlers from Joop's radiation. Hell... in a billion years, we might have to consider pushing jupiter inward a little bit (not early to where we are now, but closer), and then pushing earth and mars into orbit around it. Hell, venus too. The fresh tectonic strain may help resurrect Mars' core, and keep ours from failing... meaning both of which could potentially be warm enough from within to make up for the extra distance from the sun.
I'm sure, by then, we'll have figured out how to do all this. =)