By the way, how did the Sarpeidons know their sun was going to go nova? They obviously have a time machine, but no spaceflight. So maybe someone stepped through into the future and got fried. We can only hope it was Zor Kahn.
Presumably they'd know the same way humans have already got a couple stars lined up as nova- or supernova-candidates (and a handful of worrisome potential gamma ray bursters): astronomy and physical calculation.
The real mystery of the episode is why the Enterprise is zipping over there three hours ahead of the deadline. Were they figuring to point at the remaining population and laugh?
(Yeah, I know, they're looking there to investigate why the population's suddenly vanished, although that implies the Federation knew the planet was going to die, had a population, and yet wasn't willing or able earlier to send a ship to investigate and maybe save at least a sample of the population or its culture. Granted Star Fleet was smaller in those days, but they couldn't arrange for your classical two-man doomed outpost to read the Sarpeidon Internet?)