The Naked Time is basically a disaster movie (or, in this case, a disaster TV show) set in space: The Enterprise crew gets infected by an affliction that makes them obsessively rub their hands like Lady MacBeth on a bender and brings their innermost desires and emotions to the surface, resulting in things going very pear-shaped when Lt. Kevin Riley gets it in his head to turn off the ship's engines while the Enterprise is in close orbit over a planet in the midst of its death throes; according to Scotty, it will take 30 minutes to bring the engines back on line but the Enterprise doesn't have 30 minutes before it hits the dying planet's atmosphere and burns to a cinder.
Oh, what to do?!?!
The most entertaining part of this episode is seeing the effects of the affliction on the various Enterprise crewmen: Nurse Chapel throws herself at Mr. Spock, Lt.Riley turns into a bizarre caricature of an Irishman, Captain Kirk, in a monologue that almost qualifies as being creepy, bemoans the fact that the two women in his life, the Enterprise and Yeoman Rand, are out of his reach (the Enterprise because it's an inanimate object and not a "flesh woman" and Yeoman Rand because of the impropriety of such a relationship; as an aside, I find it interesting that Captain Kirk, who has a reputation amongst Star Trek fans as being something of a walking hormone, knew that pursuing a relationship with a subordinate just wasn't done; however, Spock in the 2009 reboot film, seems to have had no compunctions about being in a relationship with his student, Uhura; shame on you, Mr. Spock! Shame shame shame!), Spock weeps over having had to hide his emotions his entire life and how his mother must have suffered living in a society where showing emotions was considered to be in bad taste and Mr. Sulu decides to take off his shirt, grease up his torso and run through the corridors of the Enterprise with a sword and terrorize its crew, apparently in the belief that they're the Cardinal's guards from The Three Musketeers.
Clearly, Mr. Sulu has issues.
Yeoman Rand takes the helm at one point in this episode, showing that she is capable of much more than the secretarial duties she usually fulfills in the show. She is also highlighted as one of the objects of Captain Kirk's desires, tantalizingly close but, in the end, separated from the Captain by what is effectively an insurmountable gulf.
Parts of this episode that made me chuckle were Mr. Spock doing some calculations, apparently with the aid of a 23rd century slide rule of all things, Riley and Sulu attempting to prevent another crewman's suicide while half a dozen able-bodied Starfleet officers just sort of sit there and stare dumbly instead of doing anything to help, Kirk literally slapping the afflicted Spock into sobriety, Lt. Riley rewarding the Enterprise crew with a double helping of ice-cream after he has gained control of the ship and then admonishing Lt. Uhura (by depriving her of her ice-cream ration) for attempting to prevent him from singing "I'll Take You Home Again Kathleen" just "one more time" over the ship's intercom and Kirk getting his shirt ripped, not in a fight, but by Dr. McCoy administering the antidote for the affliction.