An easier way to understand this whole climate debate as 'a rise in temperature means there is more energy available in the atmosphere'. That energy can have many effects. It can cause local heating, but it can also move large airmasses around and if those airmasses are colder than the normal for that region the movement will cause a huge swing in temperature.

This is one of the main reasons the average 2.5 degree celsius change (which on an absolute scale would not make a huge difference in the first place, most people would hardly notice) is such a huge affair.

It can cause local variations that are a very large multiple of the 2.5 degrees, much like a heatpump does not require a whole lot of energy to move a much larger amount of energy around.