Sagan discusses comets and asteroids as planetary impactors, giving recent examples of the Tunguska event and a lunar impact described by Canterbury monks in 1178. It moves to a description of the environment of Venus, from the previous fantastic theories of people such as Immanuel Velikovsky to the information gained by the Venera landers and its implications for Earth's greenhouse effect. The Cosmos Update highlights the connection to global warming.

There is an extraordinary range of temperatures in the universe. This program examines the extreme lower temperature range, the temperature we live in and below, explaining how cold is essential for the formation of habitats suitable for life. Explore icy planets and moons, discover the role of cold in the Universe, and learn about the importance of ice to the development of habitable worlds.

In late Cretaceous Canada, in what will be known as Dinosaur Provincial Park, a Daspletosaurus stalks a Chasmosaurus in a forest, but loses the element of surprise and is forced to retreat. The Chasmosaurus comes across a younger Daspletosaurus, before being ambushed by a group of the tyrannosaurids. The episode then cuts to the high Arctic, where Edmontosaurus are hunted by a large species of Troodon. The theropods attack at night, separating a juvenile from the herd and severely wounding it, only to be driven away by an adult. In the morning, they return to eat the carcass of the juvenile, which died during the night. The episode returns to the Daspletosaurus, who chase and bring down the Chasmosaurus. The larger adults bully the youngsters off the carcass, forcing them to wait until they have finished. The episode then cuts to Madagascar, where a mother Majungasaurus (an Abelisaurid) and her two offspring chase a group of Rahonavis off a carcass. However, they are temporarily driven off themselves by a male Majungasaurus. But, after he steals some food from one of the young, the female attacks him, before she and her young cannibalise his body. The episode returns once again to North America, where the Daspletosaurus are waiting for the annual migration of Centrosaurus. They attack during a rainstorm, killing some of the ceratopsians. The Centrosaurus make it to a flooded river and begin to swim across, and although many make it to the other side, some are caught by giant crocodilians or are severely wounded by floating debris and thus drown, or drown for unseen reasons. In the morning, the carcasses attract scavengers, including the Daspletosaurus. A montage is then shown of Daspletosaurus and Majungasaurus, the narrator saying that together, the tyrannosaurids and abelisaurids were the last of the killer dinosaurs.

In the fourth episode, Professor Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century. After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he sees how mathematics was itself thrown into chaos by the discoveries of Kurt Godel and Paul Cohen, before completing his journey by considering some unsolved problems of maths today, including the Riemann Hypothesis.

The Pythagorean Theorem is simple: x2 + y2 = z2. In this form, the equation can be solved. But what if the 2 is replaced with any positive integer greater than 2? Would the equation still be solvable? More than 300 years ago, amateur mathematician Pierre de Fermat said no, and claimed he could prove it. Unfortunately, the book margin in which he left this prophecy was too small to contain his thinking. Fermat's Last Theorem has since baffled mathematicians armed with the most advanced calculators and computers. Andrew Wiles methodically worked in near isolation to determine the proof for this seemingly simple equation.

Questions are raised about the search for intelligent life beyond the Earth, with UFOs and other close encounters refuted in favor of communications through SETI and radio telescope such as the Arecibo Observatory. The probability of technically advanced civilizations existing elsewhere in the Milky Way is interpreted using the Drake equation and a future hypothetical Encyclopedia Galactica is discussed as a repository of information about other worlds in the galaxy. The Cosmos Update notes that there have been fewer sightings of UFOs and more stories of abductions, while mentioning the META scanning the skies for signals.