The Sea Around Us (1953) is an Oscar-winning documentary directed by Irwin Allen, which just aired on TMC. At the end of the film, there was a warning about rising temperatures at the poles, and if all of the ice on Earth melted it would raise sea levels 100 feet, wiping out coastal cities. The documentary puts the beginning of this climate change around 1900.
I’m putting this in MPSIMS because it’s just something I wanted to share.
The first prediction of global warming due to increased human production of carbon dioxide was made by Svante Arrhenius all the way back in 1896.
Growing up in the 1950s and 1960s the possibility of global warming was being discussed. There was briefly some question in the 1960s whether solar cycles and increased particulate matter in the atmosphere might outweigh increased carbon dioxide and cause a new ice age, but by the late 1970s the warming model had prevailed.
I recall in the late-'70s/'80s that there were fears that global warming might induce another ice age by shutting down the thermohaline circulation. That was fine by me, since I lived in Southern California and was a skier! 
Here is an article from 2005. A caveat though, it’s New Scientist. So TIFWIW.
Isaac Asimov was often writing about climate change.* One of his articles on it appeared in Penthouse(!) in 1971.
The writing has been on the wall for a very long time.
Yep. In fact it’s rather shocking today how little was quantitatively known about the effects of greenhouse gases and where they stood relative to other climate forcings. It was certainly understood in principle, but no one knew (much less could prove) that in the 1960s and early 70s global warming was well underway and was being masked by atmospheric particulates, notably sulfate aerosols. Forward thinkers like Hans Oeschger were among the first to understand the risks of climate change; as a pioneer in ice core research, he was the first to establish (in 1979) the low atmospheric CO2 levels associated with ice ages.
In 1975 the National Academy of Sciences issued a report called Understanding Climatic Change: A Program for Action which said that the science at that point “didn’t even know the right questions to ask” and recommended a major program of research funding around climate change. It was this period of research, culminating in the first IPCC report in 1990, that really opened our eyes to the impacts of anthropogenic climate change. Even so, that first IPCC report seems primitive, hedging, and speculative today, in contrast to the increasingly better qualified and better quantified conclusions of subsequent reports. Indeed some have said that the IPCC’s job is done as far as the three general working groups on climate change (the science, the impacts and vulnerabilities, and mitigation strategies), and that in the future they should focus on specialized reports, like the one on extreme weather.
That article discusses the Gulf Stream – technically the Atlantic Meridional Overturning Circulation (AMOC) – which is only a small part of the global thermohaline system. And its effects are mainly along the east coasts of the US and Canada and, after it splits off and crosses the Atlantic, western Europe. The effects on western Europe are arguable; some think a weakening of the AMOC may precipitate stronger storms in Britain, and ironically, at least one summer heat wave there was attributable to pressure system patterns caused by a weaker AMOC. There’s an article about various aspects of it here.
P.S.- What’s wrong with New Scientist?