> it continually increases variance in the system as warming increases

This is strictly false. A consistent warming trend reduces the occurrence of extreme cold events. This will narrow the range of temperature fluctuations, which directly reduces the time derivative of temperature variance.

Also, oceans redistribute heat more efficiently due to climate change. This causes the temperature gradients between regions to weaken. Once again the time derivative of temperature variance is reduced. Empirically, one can observe this decrease in temperature variance in the tropics.