Toward Ecosophy

The southern hemisphere faces a rather different situation, because you don't have an ice-covered ocean at the south pole, you've got a continent with a mile or two of ice heaped on top of it. I'd expect heat transfer to the south pole to pick up, too, but it's got much more ice to melt first. It's quite possible, in other words, that for some thousands of years the two hemispheres will have different atmospheric circulations. That said, your paleoclimatology is likely to be a good indicator of what you'll get.