The second half of Hill's book has her pursuing her US/Soviet swim, a darkly humorous endeavor in which she is spied on by some seriously incompetent FBI agents, repeatedly bangs her nose against the Iron Curtain, and ends up with the CIA and KGB simultaneously tapping her phone. No one can quite believe that she really is doing this because she wants to, and primarily because it's the most challenging thing she can think of, rather than for some dark political purpose in which she is merely the cover. (She does, in fact, have a political purpose, but it's secondary and personal: she hopes her swim might have a sort of butterfly effect on US-Soviet relations, showing both sides that they are human beings, not the Evil Other.)
However, the same persistence that makes her a great swimmer enables the swim to happen - she keeps banging down doors until both governments, rather bewilderedly, decide that maybe they can make political hay of it. She makes the swim, and the butterfly effect actually does seem to happen. So for a while Hill does a number of other swims intended to both challenge herself and act as gestures of goodwill between countries. These are all vividly described, as she faces off with sharks, ice bergs, sea snakes, ice sharp enough to slice a boat's hull in half, and her own cold and exhaustion.
But eventually, she can't resist the ultimate swim: Antarctica. This is in water so cold that no one is sure it is even survivable. Once again, she returns to the researchers and their rectal thermometers. This time technology has improved and they want her to swallow a mini-thermometer and data-gatherer, emphasizing that it's very expensive and they need to get it back, both to download the data and because it's re-usable - "Just use a plastic bag!" Cox, suspicious: "Am I the first person to swallow this thing?" The researcher assures her that she is, while accidentally also making it clear that she won't be the last.
The reason I read this book was a brief article on Cox's swim which noted that before the swim, her teeth had to be specially sealed and some of her fillings removed and replaced, because otherwise they would shatter from the cold. That, I thought, was hardcore. At the end of the book, she notes offhandedly that the nerve damage she sustained from the cold (which she only barely mentions otherwise) is repairing itself, and she's resting while looking forward to the next thing.
Once again, highly recommended if you like this sort of thing.
Swimming to Antarctica: Tales of a Long-Distance Swimmer