The Enterprise crew is thrilled to encounter the biggest comet humans have ever seen, one that's 82.6 kilometers in diameter with a spectacular tail. Learning the comet contains large quantities of eisilium, an extremely rare mineral, Captain Archer dispatches Commander Reed and Ensign Mayweather to take a little "comet-walk" with a drilling rig to collect samples. As they prepare for their mission, a Vulcan starship, the Ti'Mur, approaches unannounced. Archer hails the ship, and its captain, Vanik, informs him they are not there to investigate the comet, but rather to investigate Enterprise's interest in the comet. Although irked, Archer gracefully invites Vanik to stay and watch, but then he pulls T'Pol aside to find out what they're "really" doing here. T'Pol has no answers.
Reed and Mayweather land a shuttlepod on the comet, eager to experience the wintery world. Meanwhile Commander Tucker is disturbed to discover that T'Pol has secretly received an encrypted transmission from the Vulcan ship. He reports this to Archer, and upon his orders enlists Ensign Sato to decrypt the message.
The bridge crew takes a little time out to record a message for Tucker's nephew's fourth-grade class in Ireland, answering the students' questions about such things as what they eat in space and how they talk to aliens. Each crew member in turn responds to the topics they specialize in, but Tucker is a little upset when Archer picks him to answer the question, "When you flush a toilet, where does it go?"
On the comet, Reed and Mayweather are setting charges in the ice as the first step of their drilling operation, but they can't resist taking some time to build a snowman — with Vulcan ears. Meanwhile, Tucker reads the message to T'Pol that Sato decrypted, and realizes it's nothing incriminating, but rather an intensely personal letter. Highly embarrassed, Tucker decides to confess to T'Pol and apologize. She is uncomfortable with Tucker knowing about her situation, although he agrees to keep it between themselves. T'Pol will not even confide in Dr. Phlox when she receives treatment for a tension headache and sleeplessness, but the doctor advises that she talk to someone about what's bothering her.
In a gesture to gain the Vulcans' trust, Archer decides to invite Captain Vanik over for dinner with him, T'Pol and Tucker. The dinner does not go well, however, as Vanik just sits at the table without eating and barely responds to attempts at conversation. Archer gets fed up and abruptly asks why the Vulcans are spying on them. Vanik condescendingly denies the accusation, and Archer send him back to his ship.
After Reed and Mayweather blast a crater in the comet's surface, they begin setting up the drilling rig. But the blast shifted the comet's rotation, so Archer orders them to pick up the pace because in two hours they will be exposed to the dangerous heat of the nearby star. On the ship, T'Pol decides to take Plox's advice to relieve her stress by talking about her concerns with someone. In the encrypted letter, T'Pol was given an ultimatum to return to Vulcan immediately or her arranged wedding will be cancelled. So she asks Tucker, the one person who already knows the situation, whether she should honor her people's traditions or her obligation to Enterprise. He tries to convince her to think for herself and do what is right for her, but she insists her family and heritage must take precedence over "personal choice." She acts like her mind is made up, but Tucker is not convinced.
Having collected a core sample, Reed and Mayweather are removing their equipment when Mayweather slips back into the blast crater and injures his knee. Their pace is slowed as Reed helps the limping Mayweather back to the shuttlepod, and sunlight begins to break across the horizon. The ice begins fracturing beneath them as they take their final few steps toward the shuttle. They make it inside, but when they fire up the engines, the ice collapses beneath the shuttle and it plummets into a gaping chasm. They are now trapped, so Archer takes the helm of Enterprise to navigate the ship close enough to use magnetic grapplers to retrieve the shuttle. Captain Vanik hails him to offer assistance, but Archer refuses. Tucker manages to hit the shuttle with one grappler, but the eisilium deposits disrupt the maglock and the shuttle drops back down. Since the Vulcans' tractor beam would not be affected by the eisilium, T'Pol convinces Archer that to accept Vanik's help would be to prove him wrong about humans being arrogant and prideful. He concurs, and Reed and Mayweather are rescued by the Ti'Mur.
Archer tries to thank Vanik by offering to share the data they collected, but Vanik gives him the usual cold reply, and the Ti'Mur prepares to depart. Tucker asks T'Pol if she's ready to leave with the other Vulcans, but instead of packing, she sends a message to the Ti'Mur to convey to her family, declaring her intention to stay aboard Enterprise.