I read this story years ago in an anthology that I believe was published in the 70s, and it’s haunted me ever since.
An alien spacecraft is travelling the galaxy, making observations of astronomical phenomena. The come to realize that a star they’ve visited before has become unstable and will soon destroy itself, so they decide to park a safe distance away and collect data on the event. The star, as it turns out, is our sun.
The crew is populated by aliens from a wide variety of planets and cultures, and the Federation to which they belong is very old – millions of years is implied. One of the crew notes that, the last time one of their vessels visited the star tens of thousands of years ago, the third planet was inhabited by some semi-intelligent ape-like creatures. It might be nice to collect a bunch of them before the star dies so they could be resettled on another world, to continue to evolve.
On visiting Earth, the crew is astonished to find that, in their absence, the ape-like creatures developed intelligence, civilization, and space-faring technology. In fact, the planet is deserted, since humans knew the sun was going to die and piled into their own spaceships to escape. There’s a cool adventure sequence where the aliens figure all this out.
Some of the crew are overjoyed to find out that a new sentient species has been discovered, but others are more circumspect, noting that, elsewhere in the universe, species develop civilization and technology much more slowly (over millions of years, not tens of thousands), so their violent tendencies tend to diminish before they develop potentially-destructive technology.
They locate the human fleet that is fleeing the doomed sun and decide to make contact.
In a chilling final scene, one of the crew half-jokingly muses (paraphrased): “I’m a little afraid of these people. What if they decide they don’t like our culture?” Followed by the last line: “In forty years, his little joke didn’t seem quite so funny.” 
It’s been one of my most fondly-remembered stories for years. Any ideas on author or title? For a change, I’m pretty sure it’s not Bradbury or Heinlein!
