In the episode "Wink of an Eye" Kirk once again finds himself face to face with a hideous space alien.
Much like the matriarch of the society featured in the prior episode who wanted to make Dr. McCoy her husband, this alien apparently took over the Enterprise with the intention of reproducing with Kirk, and making him her King.
She stated that this was necessary for the survival of her race, because the men of her society no longer reproduce with women.
Kirk angrily argues with her and seems to imply that having sex with her is equivalent to death:
Alien Queen: We'll be kind to you, you won't be harmed. I do like you... Captain, we have the right to survive.
Kirk: Not by killing others!
Killing others? What is he talking about?
The only person who died was an Ensign who died from accelerated aging after being injured, but that's apparently a situation that only occurred if a person was injured shortly average being "accelerated" to the speed of this hyper-fast race.