I like to imagine that this is how things would look if we entered a Karadashev type III civilization's light cone: One day, in a small quadrant of the galaxy, we'd notice starts "shutting off", simply going dark. After a few months, our astonomers would confirm their new model: the amount of stars going dark is increasing. Days later: the rate of increase itself, is increasing. One day we'd wake up, and a small port…
Almost immediately, they have no more use for small rocky gravity-well planets, or even for stars. They live in Oort clouds where thermal noise is low and cold is plentiful.