Yes, this seems inevitable, and given Europe's relative historical contribution to climate change, I think we have a moral obligation to welcome some, as (to some extent) their right, not charity. An issue, however, is that immigrants tend to gather in crowded hot cities near sea-level, just the places we should plan to slowly depopulate, while it's rarer to see African faces in sparsely populated upland rural areas, where there are more empty houses and older people needing services. Research about climate migration focused mainly on where people will move from, not enough about where it would make most sense for them to move to.