Wow; this is exactly what the Romans did during the Roman warm period. They gave up their industrial society, and the planet grew colder. But because they were no longer industrialized, they could no longer defend the Empire and were overrun by barbarians.
But hey, they stopped global warming.
The same thing during the High Middle Ages; they had all this industry that built the Cloth Halls and Guilds, and the beautiful cathedrals of Western Europe. Trade flourished in the Baltic through the Hanseatic League, and the Vikings raised cattle in Greenland. But all this industrial activity caused global warming, and so they ceased the activity. Thus, the planet cooled, and in the colder conditions, reduced harvests could no longer feed a now weakened population. This led to the Black Death and fall of the Medieval civilization.
But hey, they stopped global warming.
Excellent parody!