There is an article in New Scientist today, describing a new paper in Science by Büntgen et al. This is a tree ring study using samples from France, Germany and Austria to recreate temperatures and precipitation for the last 2500 years. There is a hint of a lack of a Medieval Warm Period:
From AD 250 to 550, the climate flipped, from one decade to the next, between dry and cool, and warm and wet. "Such decadal changes seem to have the most impact" on civilisations, Büntgen says, because they harm agriculture but are not prolonged enough for people to adapt their behaviour.
The climatic turmoil coincided with political upheaval and waves of human migrations. By AD 500, the western Roman Empire had fallen.
In other notable periods, the relatively stable medieval society was characterised by more constant climatic conditions. But the Black Death coincided with a wet spell and the disease spreads faster in humid condition