Book probably from between 1950 and 1980. A nuclear bomb destroys the Panama Isthmus. The Gulf Stream stops, disastrously changing the world's weather.
Central Passage by Lawrence Schoonover, published in 1962.
Annoyingly I cannot find my copy to provide supporting quotes, but I managed to find a review in P. Schuyler Miller's article The Reference Library in the July 1962 edition of Analog:
As a matter of fact, the gimmick in "Central Passage" is a good one and relatively new in non-SF circles. The "20-Minute War" of "Central Passage" - which is touched off by a prestige-seeker in a Red satellite - destroys seven hundred miles of the Isthmus of Panama. The Gulf Stream begins to pour into the Pacific, instead of circling back to warm the coasts of North America and Europe, the clouds of dust and steam from the holocaust shut off the sun's radiation, and the world is in for another Ice Age.
In the early part of the book the author follows the fortunes of two families: the Youngs - American Navy, stationed in Panama but fortunately in Jamaica at the time of the touch-off, and the Bolducs - Gaspesian fishermen with a tradition that may go back before Columbus. The fortunes of Narcisse Bolduc, his wife, and their ten children as they make their way from the Gaspe down the ruined coastline of the United States to the stub-end of Guatemala, where an international task-force is trying to replace the isthmus, are especially interesting, if unsurprising to Old Holocaust Hands like the readers of Analog.
Meanwhile the author has been dutifully, if not very subtly - to us OHH - planting clues to the Big Shock that is the theme of the last third of his novel, "The Intruders". Little Bill Young Jr., born at the very moment of the Panama burst, is incredibly precocious. So, it appears, is Angelique Bolduc, born as the radiation from the bombed cities of Canada began to bathe the Gaspe. They have brown eyes, they see the ultraviolet spectrum - another of the author's points that is precisely the reverse of what he intends - they are telepathic and extraordinarily intelligent, they mature at a terrific rate. They are "Homo Supersapiens" and in the final chapters their parents see them hunted down and murdered in cold blood.
While I don't think that this is the book you remember, I have to mention the 1925 novel Atlantis (German Wikipedia) by the German classic SF writer Hans Dominik. It explores exactly the idea that large explosions (meant to widen the Panama Canal) destroy the Isthmus, leading to a rerouted Gulf Stream. This may well be the first time this idea was explored. I'm paraphrasing the German Wikipedia page here:
Through a mixture of intrigue, scheming and sabotage, the planned widening of the Panama Canal by gigantic explosions is performed in a dangerous fashion, braking up the Isthmus between the Americas. The gulf stream is rerouted and a panic ensues in Northern Europe. A mass exodus threatens a decline of the white race. The damage is reverted though by the heroic deeds of a German with telekinetic powers, who also raises Atlantis in the process.
I enjoyed reading Hans Dominik 50 years ago. When I was revisiting some of his work as an adult though, I found it rather unpalatable. While I'm all for making heroes of engineers, the second underlying theme that's driving the stories is his chauvinism. Some of that had been edited out in the editions I was reading back then; being confronted with it in newer editions spoiled the experience.