The mad rush to get there would likely extract a heavy toll.
Rain patterns and extreme weather events are the things to really worry about. Temperature changes alone can be mostly dealt with by planting different crops.
Climate refugee situation will dwarf any war refugee issues. They claim "invasion" now, but this one will be an actual invasion.
That one may not be out of the woods yet.
Basically like how when people can't breath good you put them on oxygen to keep them alive only getting oxygen into the blood is the bottleneck rather than into the body.