As in a "perfect storm" scenario, several disparate factors coming together at a single moment were probably at work in all cases of societal collapse. A combination of overpopulation, war, drought, over reliance on a single food source destroyed by the drought or a blight, then disease. Throw in a now well established nasty swipe by Mother Nature in the form of the Santorini volcano and tsunami and you have the utter destruction of a civilization (which is usually taken to mean urban living that allows the flourishing of leisure and the arts).
The idea that a couple degrees rise in average temperature alone could bring down a civilization is fantasy. Now, a five degree temperature drop? That could be a real problem.
Santorine was 300 or 400 years before the period under discussion. I am going to check out my Volcano Encyclopedia to see if I can find something else. Of course, volcanoes are not the only possibility.