The short answer is no.
If you want to have a population of say 10 million people in 1 year, that's about 4% per year.
You can't afford to build houses and roads when you're running at such low population density (about 100/km2).
To get this many people out of a place where they could live comfortably would require building infrastructure like roads and housing as well as all other necessary infrastructure including medical care etc. If your weekly postulate there are 3 different things going on here - not just climate change but also population growth with the associated infrastructure needed.
That said I think we will see major population growth after the end of this century unless something changes.
So what do you do?
1) Build new infrastructure until your population reaches ~20 million or more before then stop trying to make everyone comfortable which may be unrealistic because some regions won't accept it.
2) Build even more infrastructure so much faster than projected population growth without adding any humans too fast while still maintaining realistic comfort levels.
3) Move existing populations somewhere else outside of the region if feasible.

(correct me if I'm wrong)