With a warming planet, the long term trend (thousands of years) would be more rainfall at the mid latitudes (tending to offset the droughts and forest fires, think back to dinosaurs in lush N American forests here). Short term as you say, the melting of polar ice is reducing ocean currents, tending to increase mid-latitude drought.

https://scottvern.medium.com/what-the-worlds-weather-and-farming-may-look-like-in-2100-9d3e30ab18bf