In order to melt the southern ice cap, it will take much more than a couple of degrees warming as the southern polar region stays well below freezing, year round. It should be noted that palm and other tropical plant fossils and remains have been found under the ice there. That area was once warm. Who knows where it was relative to the polar apex at that time?

Warming of the globe would allow farming on much more northern lands. That would allow us to increase food supplies. (Some experts think we could feed 29 billion folks now)

I do not think that global warming would cause many problems at all. That is, it the golbe were warming. It seems as though we are actually cooling right now.

Our real problems will be economic and cultural in the foreseeable future.

Don’t forget that water vapor is also a greenhouse gas, so increased ocean evaporation can also lead to more rapid warming as more heat from Earth gets trapped in the atmosphere. There is no evidence that increased cloudiness will lead to a ‘very cool period on Earth’. Also, there is evidence that temperatures will increase about 4 degrees in 100 years. Beyond that, it is difficult to predict temperatures because we don’t know how humans will respond to the climate problem and mitigation can reduce warming significantly. I would not however agree with you that a 40 degree temperature change is unlikely. Look at Venus. Venus has a ‘runaway greenhouse effect’. Venus used to have oceans, but now it has a very dense atmosphere and a surface temperature of about 400 degrees. Venus is a lot closer to the Sun, but provides an important example of one possible future scenario.