The atmosphere is not a simple system, but an intensely complex one.

One effect of 'warming' (i.e. increasing the total amount of energy in) the atmosphere is to increase the total amount of energy in the system (doh!) - this leads to more turbulent air flow. Also as the polar ice melts, the coolness (lack of heat!) liberated mixes with the warmer air - thus driving the turbulence.

Thus we will get both higher and lower peak temperatures for some time until a new 'static equilibrium' is achieved. More storms, more rain, more snow in some parts, more dry weather in others. We currently have a Category 5 Cyclone rumbling about the North end of Queensland about to pass near Cooktown - these used to be very rare - Cyclone Tracy in 1974 was a previous example.