Read The Uninhabitable Earth.
Covers a lot of this. The biggest part of this issue is contained in your question: You think climate change's effects will be limited to warmer temperatures and drier rivers. It won't.
Climate change will exist as a variety of effects, from more extreme weather (of all types) and rising sea levels through to droughts, famines, wildfires, erosion, declining biodiversity and migration. To give you a sense: a projected 140 to 200 million people are expected by the UN and World Bank to become climate refugees fleeing their home by 2050. The Syrian War, for reference, caused a total 1 million refugees.
It is much, much worse than you can imagine.