It won't be a smooth change to the new conditions either; there will be centuries of instability and infrastructure and agriculture will have to adapt to obsolescence every few decades.
I'm not a climatologist but I do know some of the reasons why:
The thermal gradient between the equator and the poles (a major driver) will weaken - the poles will heat up more quickly.
Ice at the poles drives some ocean currents.
Temperatures at different heights in the atmosphere will be affected differently.
Increased evaporation from oceans but higher ambient temperatures will change cloud formation unevenly.
Nights will cool down more slowly due to the 'blanket' effect of CO2.
The overall effects are interconnected of course, which is why there is so much work on modelling and so much work still to do.
Edit: I forgot to mention the effects on vegetation and landscape that will also feedback unevenly into the climate. e.g. rainforests depend on and generate a lot of rain; a rainforest may hit a tipping point where it is no longer viable and rainfall will then collapse over a large area.
[1] Here's the latest, from AR5 in 2014. It's a little out of date, but it holds up fine as an introduction (mostly what's new since then is "we've done nothing, so things are now even worse"). AR6 is due out in 2022. https://www.ipcc.ch/site/assets/uploads/2018/02/AR5_SYR_FINA... (3.5 MB)
I imagine you'll get more rainfall over oceans; air currents over land will hold onto moisture until they blow over oceans, cooling them. I also imagine you'll get more rainfall on the sides of mountains which are already regions where warm, damp air rapidly cools causing precipitation.
Please don't take this as truth, I'm just theorizing, I'm not qualified.
Any climate conversation in a nutshell.
You get mega droughts followed by mega flooding (depending on region).
Those are tied to global increase in mean temperature.
Shifts in rain patterns due to these oscillations have always occurred, what does this mean?
[0] https://ourworldindata.org/grapher/number-of-natural-disaste...
That means climate change is a natural function going back billions of years. See:
https://www.sciencedirect.com/topics/earth-and-planetary-sci...
https://www.sciencedirect.com/topics/earth-and-planetary-sci...
https://www.sciencedirect.com/topics/earth-and-planetary-sci...
Here's hurricane data in US going back to 1800s: https://www.aoml.noaa.gov/hrd/hurdat/All_U.S._Hurricanes.htm...
(Note, we didn't have instrumentation for measuring exact strength of hurricanes prior to satellite era in the 1970s)
So I am sorry chrisco, but I am not sure what you are alluding to?
It's not the absolute we have to watch out for. It's the rate of change!
Yes and no. It explicitly means that the average temperature, globally, is increasing. Drastically so.
Extreme weathers is just one of the side effects. Others include: ecological collapse, insane scale population migration, catastrophic sea level rise, etc, etc.