Events like this become more frequent:

https://www.scientificamerican.com/article/deadly-african-he...

If you shift a normal distribution to the right even a little bit, the frequency of tail events above a fixed threshold (in this case, wet bulb temperatures exceeding the human survivability limit of 35 degrees celcius) increases more than linearly.

This is especially an issue near the equator, which will lead to climate refugees seeking colder climates, north and south.

If that's all that happens then humanity has been lucky. At the other end of the scale, billions die of starvation, wars over resources, etc.