The medieval warm period did not affect sea ice at all.
It also did not affect the global temperature at all.
On your weird definition of global?
It was a localized effect in such a small area that the global average didn't even move.
No it wasn't. We just have no data about the _global_ temperature at that time, but we have reports from many places of the world, notable China and Japan that it was warmer than normal there, too. So: very likely it was at least on the northern hemisphere a global phenomenon.
So: the lack of written evidence, because we have none from Inka, Australians, Africans, does not mean it did not happen there.
And: if you talk about a/the medieval warm period, it would be cool to add which one you mean. There where three AFAICT.