I think we’re kind of stuck with mostly northern hemisphere data since there aren’t many good sampling locations down under.
The rate of increases are notable just because of their lack of periodicity yet the graphs show that each period of cooling began nearly precipitously which might make one question what shut off the cause of warming so suddenly.
For the LIA cooling, sunspot numbers famously indicate solar activity minima that no doubt were a primary cause. I hazard an unschooled guess that the MWP resulted from variability of the thermohaline circulation. Reduced bottom water formation would allow more heat to stay in the atmosphere, and because the North Atlantic is where a lot of the bottom water forms, this would be the strongest area of impact.
But I don't think there's much I can produce to support that idea.