The crew's attempts to save the inhabitants of Penthara IV from the devastating aftereffects of a massive asteroid strike are interrupted by the arrival of Berlinghoff Rasmussen, a purported historian from the 26th century, who claims to be studying their era. But the rather curious nature of Rasmussen's questions about the 24th century, and his interest in gathering- and stealing- technological "artifacts" from the Enterprise, make Troi and the others increasingly suspicious of his origins.
On the way to Penthara Four, the Enterprise encounters a temporal distortion, and discovers a small pod containing a single human. Once aboard, the pilot identifies himself as Professor Berlingoff Rasmussen (Matt Frewer), who has come back from the 26th century to study history. Rasmussen sets about examining the ship and interviewing the crew, but reveals little about himself. This is necessary, he insists, because he does not wish to alter history.
The Enterprise arrives at Penthara Four, which is suffering a planetwide drop in temperature due to dust kicked up by an asteroid impact. The crew prepares to use the Enterprise's phasers to drill into the crust and release carbon dioxide, thus increasing the greenhouse effect. The plan works, and Rasmussen, claiming this is a very important historical event, is overjoyed. Rasmussen continues his interviews, in a somewhat irritating manner, and even makes a failed pass at Dr. Crusher.
After a short while a series of earthquakes and volcanic eruptions begin rocking Penthara Four, an unanticipated result of the drilling. The volcanic ash being thrown into the air is dense and threatens to block out the sun and cause an ice age, killing thousands. Geordi and Data come up with a plan to sweep away the dust with an ionizing phaser blast into the planet's upper atmosphere. There is no margin for error and if executed imperfectly the blast will burn off Penthara Four's atmosphere, killing all twenty million inhabitants.
Picard is prepared to forgo his temporal-prime-directive principles to save thousands of lives, and asks Rasmussen to reveal the outcome of the mission. The professor refuses, pointing out that in his time, all those currently alive on the planet have been dead for a while (regardless of their cause of death), and he dare not risk altering history. Picard accepts Rasmussen's reasoning, after some heated discussion, and decides to try Geordi and Data's plan, which succeeds.
Having finished his study, Rasmussen heads to the shuttle bay to leave but is surprised to find the Enterprise senior staff there blocking his way. Picard mentions that several small items (a tricorder, for example) are missing from around the ship, and he believes Rasmussen is the culprit. Rasmussen refuses to allow his ship to be searched, but eventually agrees to let Data inside; Picard acknowledges Rasmussen's reasoning that Data can be trusted not to mention his discoveries about the craft to the rest of the crew.
Data discovers all the stolen items inside, and Rasmussen aims a phaser at him. The professor reveals that he is not a historian from the future, but rather a disgruntled inventor from the past—in particular, 22nd century New Jersey. Rasmussen stole the time pod from its real owner, a 26th-century historian, and planned to take 24th-century items back to his own time where he would reverse engineer them and release them as his own inventions at a rate of one per year. He now intends to take Data along as a further invention, but Rasmussen's phaser has been deactivated by the Enterprise's computer and he is easily subdued.
Data escorts Rasmussen out of his ship and into the shuttle bay, carrying the stolen items. Moments later, the now empty time pod automatically returns to the time from which it originated. Stranded in time, Rasmussen is left to the mercy of 24th-century justice.