Considered from a global perspective, as you say, global warming renders some places less inhabitable but others more. If humanity were a single body of people who could all relocate at will across the globe, there'd still be massive costs involved to relocate hundreds of millions, if not billions of people, but there wouldn't necessarily be a real fundamental problem - or at least, potentially there wouldn't be, I'm not sure that we can say with any degree of certainty that the gains in temperate places like Russia and Canada would fully outweigh the losses elsewhere.

In the real world, though, the people living in those temperate areas that would see huge immigration under this plan really don't want a single global body and don't want their respective national identities to dissolve, so there are limits to how much immigration they will accept. And their objections against, not even the current levels of immigration but a hundred times as much of it, are likely much, much stronger than their objections against the kind of sacrifices that are required to seriously hit the brakes on global warming. And for good reason.

Now if you say, screw that, I'm neither going to accept mass immigration into my country, nor am I going to bother making an effort to fight global climate change, then the only remaining option is to embrace the position of 'eh, who cares, let hundreds of millions starve to death in their own countries or else drown or get shot while trying to force their way into ours, all due to a phenomenon that we bear exponentially more responsibility for than they do'.