The mediaeval thing was a combination of el nino type events, one down there and something else North Atlantic I vaguely remember. It was followed by the "little Ice age", neither of which look anything like what we're seeing now.google it.
https://en.wikipedia.org/wiki/Medieval_Warm_Period. They were fairly short term wiggles.
The problem we have now is around the rate of rise, the lack of time for species to adapt, and the lack of any prospect of reversion to any mean without something like a nuclear winter. We should expect bad things coming to humans - like droughts, water wars, mass migrations, destruction of coastal cities by sea level rise. They're talking about building an 80ft high sea wall in Jakarta Indonesia,
Seas are predicted to rise a foot by 2050, regardless of how much global carbon emissions can be reduced. Why is this happening, and what can we do to adapt?
www.nationalgeographic.com
The speed is a problem, because of the flip effect, positive feedback loops taking us to positions where there's no route back by mere reversal of the drivers..
As Sir Lord God Attenboro said, we'll be making things very difficult for humans, and its highly probably there will probably be some sort of human-caused extinction, but the planet will recover and get on fine without us for quite a while yet.
I remember seeing a TV prog explaining how, after only of the order of 10k years, there will be surprisingly little sign that we were ever here.
I don't mind. I'll be long gone.