In fact, many hypothermia victims die each year in the process of being rescued. In "rewarming shock," the constricted capillaries reopen almost all at once, causing a sudden drop in blood pressure. The slightest movement can send a victim's heart muscle into wild spasms of ventricular fibrillation. In 1980, 16 shipwrecked Danish fishermen were hauled to safety after an hour and a half in the frigid North Sea. They then walked across the deck of the rescue ship, stepped below for a hot drink, and dropped dead, all 16 of them.
Reddit has some discussion of this, largely dismisses the 16 Danish fishermen story as a myth (though points to a couple of published sources as well).
http://www.hse.gov.uk/research/othpdf/500-599/oth519.pdf (UK compendium of sea immersion rescue issues, no mention of Danish sailors).
Basic Essentials: Hypothermia, by William W. Forgey, 1999. Does include a mention, but includes no citations, references, footnotes, or endnotes.
Having read several of Bryson's entertaining works, I know that he is not a rigorous researcher of the details.
The link I gave was to "Hypothermia and Cold Stress" by Evan L. Lloyd, 1986. It shows a citation to Lee and Lee 1971. I am unable to track down that reference based just on free internet searches. According to Lloyd's recounting, the rescuees did drink some alcohol. I can see how upon retelling that might be turned into a "hot drink."
I am quite willing to say that the previous poster heard about the Bryson story and the false details from that. However, I would rather state that the details of the story - that being of Danish fishermen - were wrong rather than the point of the story, which is the death of people after they have been rescued. In any case, the parent poster said nothing about Danish fishermen.
Even if "Lee and Lee 1971" citation I pointed to is too vague of a confirmation for you, the HSE report gives many examples of "post-rescue collapse and death" from both Allied and Axis sources, including from ship-wreck survivors (Critchley 1943).
I think it's unsafe describe the situation in a way that could be described as implying an urban legend, which is why I've specifically said that the details are wrong, and pointed to places where the details are correct. (To be sure, you are not doing that. I write this to explain why I wrote it as I did.)