The Enterprise is in orbit around a planet that Spock's sensors indicate has been lifeless for thousands of years following a global disaster. The crew is surprised to hear a voice in their minds introducing itself as Sargon and inviting Kirk to beam down to the planet. At the extreme limit of sensor range, a hundred miles beneath the surface, Spock detects a power source. Sargon declares that they have found him and that he will make it possible for transportation to take place. Kirk tells Spock that he plans to go alone but the ship's power cuts off, returning only when he agrees to take Spock with him. They go to the transporter room to find McCoy and Dr. Ann Mulhall waiting. They have also been 'summoned' and Sargon transports the four of them down, leaving two security guards on the transporter pad.

They find themselves in a vault where a glowing sphere on a pedestal advises itself to be Sargon. He explains to the landing party that he and two other beings are now the only survivors of the planet's best minds that were stored there after a war that devastated the world half a million years ago. They once had bodies but are now creatures of pure thought, living inside the globes like the one they can see. Sargon takes control of Kirk's body, transferring Kirk's mind into the globe in place of his own. McCoy's tricorder indicates that Kirk's body is starting to burn up but Sargon insists that he and the other two survivors need the use of the bodies of Kirk, Spock and Mulhall.

Sargon takes them to another room where two lines of the spheres are stored but only two of them are glowing, the ones that belong to his wife Thalassa and a former enemy called Henoch. He tells them that they only require the bodies for long enough to construct artificial ones to house their minds. As Kirk's body starts to weaken rapidly Sargon relinquishes control and returns to his sphere. The three storage globes are moved to the Enterprise where McCoy oversees the mind transfers. Henoch, in Spock's body, prepares three hyposprays to counteract the rise in metabolic rate but Nurse Chapel notes that Sargon's appears to be different from the other two. Henoch uses mind control to make her ignore the fact and lets her know that he intends Sargon to perish so he can keep Spock's body.

The three aliens start work on the artificial bodies but Kirk's body soon starts to tire and Sargon goes to get his injection. Henoch persuades Thalassa that they should keep the real bodies as the artificial ones will not have the same feelings. Thalassa goes to Sargon in the briefing room to put forward a case for keeping the bodies but he is extremely ill and collapses. By the time McCoy and Chapel arrive he is dead. They are able to keep the body alive but Kirk's mind is trapped in the sphere. Thalassa offers to save Kirk in exchange for being allowed to keep Mulhall's body but McCoy refuses. She tries to affect his mind but suddenly realises what she is doing and stops. They hear Sargon's voice telling them that he has transferred his mind to the ship's computer.

Thalassa tells McCoy that Sargon has a plan to save Kirk and asks him to leave the room. He feels the ship tremble and sees Chapel walk out. When he returns he finds that Kirk and Mulhall have had their minds restored and that all three spheres have been destroyed. Kirk orders McCoy to prepare a lethal injection for Henoch as Spock's mind is dead. On the bridge, Henoch has taken control of the Enterprise. McCoy tries to inject him with the hypospray but Henoch stops him, ordering Chapel to inject McCoy with it instead. She takes the hypospray and before Henoch can react plunges it against Spock's body. Henoch desperately tries to transfer his mind to another body but Sargon prevents him, trapping him inside Spock's body until he eventually dies.

Chapel shudders and Spock immediately stands up again. Sargon explains how he convinced McCoy , and therefore Henoch who was able to read McCoy's mind, that the injection was lethal but was, in fact, only a sedative. Spock shared Chapel's mind after the spheres were destroyed so that Henoch would have nowhere to go and was returned to his own body when Henoch died. Sargon and Thalassa come to the conclusion that they can't exist in artificial bodies after experiencing feelings once again and are allowed the use of Kirk's and Mulhall's body for one last embrace before they allow their minds to dissipate and die.