The future, and I'm not talking about 2060 or 2200, I'm talking capital-F Future on scales of hundreds of millions of years, is going to involve some serious backpacking problems.
The Sun is not eternal. It's a spherical fusion reactor with a fixed amount of fuel, that will eventually run out, and a long, long time before that happens, it's going to get hot out here. In about one billion years, Earth will have left the habitable zone entirely (and that's assuming we can do something about the carbon cycle), and we'll have to either give up on the Earth entirely, or move it.
To move the Earth, you can't touch it. Putting, say, a giant ion drive on the equator and turning it on for a few minutes at dawn every morning would wreak total havoc, even with an engine way too weak to be worth anything. So you need a tug boat-- something massive, but not something with an atomosphere that could get chopped up running a big rocket engine day in, day out, and preferably something that wouldn't be creepy to look up at every night...
Oh hello there, moon.
Now, rocket fuel. You need, um, LOTS. So much that the whole thing's a non-starter unless you could somehow do direct mass-energy conversion on the moon rock itself. Good thing it's the year 500 million AD, because antimatter flippers come in twelve packs down at the corner shop. (Halloween is hell lately.)
So you build a massive antimatter engine right into the regolith. Say it with me, that's no moon, it's a space station. Rocket ship. Tugboat. Whatever. This will probably not be the best thing in the world for tides, so it's not totally without side effects, but it's better than everyone having to crank the AC up to "thermodynamic atrocity".
With the tugboat moon, we can pretty much outlast the sun's pre-red giant temper tantrums, and in the off season between Earth draggings, maybe we can pull Venus out to someplace respectable where we can land without special hell planet gear. Heck, let's put all the rocky planets in the habitable zone. The moon is now our own private planet magnet.
That is, assuming the sun lasts that long.
As I picture our distant future counterparts rearranging the rocky planets in the solar system with a moon with a rocket engine strapped to it, (presumably, occasionally feeding it asteroids and dwarf planets, sorry Pluto) I start to seriously doubt this whole Dyson Sphere business, where presumably some advanced alien race would have already done this: build a 1-AU radius sphere around a star, soaking up all the radiation and expelling waste heat. Trouble is, this is a massive undertaking, requiring entire stars getting melted down for slag to build into the structure.
And if you're melting down stars to build one, why the heck would you use one as your primary reactor? The sun is a massive hydrogen reserve with tremendous amounts of fusion energy on tap, and you're a super-advanced technological race that can demolish stars if you need to, and you're going to use it like the boiler in a steam engine?
No, my guess is that, at some point, civilizations reach a crossroads, where they can either keep their home star around for sentimental reasons, or they can have it undergo a controlled demolition and harvest the mass-energy directly.
This of course is little help to SETI, which is highly unlikely to catch middle-aged yellow dwarf stars inexplicably blinking out of existence with all the fanfare of an apartment complex demolition.