I wonder if there is some connection between variance in temperature extremes and average warming? I feel it could either be due to the same underlying cause or

I wonder if there is some connection between variance in temperature extremes and average warming? I feel it could either be due to the same underlying cause or because larger variance will mean the average warming will appear larger. I suspect the former (i.e. it really is warming faster in the poles). I guess one could think of Siberia as a canary in the coal mine for global warming. Not that we should need one.