The way it works, is that the mutations that already occurred, either work well, or less well, when the conditions change.
If the RANGE of the changes is WITHIN the range of variation in the population exposed to it, then, some survive.
Those of course are now in possession, by the process of elimination, of genes that work in the new conditions.
This REMAINING population that managed to be squeezed through the filter of selection pressures, is now what's left to work with.
The temperatures would need to be pretty dramatic though for a human, as is, to NOT be able to survive it in of itself.
What is NORMALLY the TRUE pressure, is what to eat as a result of the change in temperature, as crops that worked great before, are now not in THEIR range of adaptation.
Given worldwide food distribution already extant, the wealthier areas should be OK, but the impoverished areas will be whacked hard.
On the flip side, if they are currently impoverished due to too dry/hot a climate, the change in climate can mean they get more rain, and reap a bonanza of new crop options they can then also SHIP to the areas with more infrastructure and less food...reversing their fortunes, etc.
For famine ravaged areas, the members of the population currently fighting weight gain, the one's who get fat eating almost nothing, now look pretty healthy compared to the Twiggy-esque previously genetically blessed demographic, as, gaining weight on almost nothing is now a desirable trait.
And so forth.
If conditions change back in the future, rampant obesity would then be a huge problem, again.
That's a nice analysis, TJ. Too many people are in a near-panic.
Anytime there is a genetic bottle neck, historically, in evolution, it decreases the resulting genetic diversity.
So, while the REMAINING populations tend to BE better adapted to what we see THEN, they are therefore NOT going to be as likely to have the diversity required to adapt to FUTURE changes, etc.
The shrinkage of land that accompanies the enlargement of the seas, leads to mass migrations of people from flooded/now uninhabitable areas, to higher elevations/better food supply regions, etc.
If you think the flood of refugees we see now is bad, from war zones in the middle east for example, wait for what follows if refugees from environmentally related areas are added to the mix, and wars to gain/defend resources, etc, ensue.
In a worst case scenario, it can be a destabilizing force worldwide.
So, global climate change is still no joke, but, in the short term, much of what we are more likely to see is a SLOW process that sneaks up on those who don't take it seriously.
Denial is many societies' primary response to long term trends, as it avoids needing to make sacrifices NOW. That in turn MULTIPLIES the rate of sacrifice required LATER, to make up for the lost response time.
It transforms potential initial proactive measures, on a planned, methodical basis, into subsequent emergency measures performed on a reactive basis: Phased zoning law changes vs emergency evacuation procedures, for example.
Honestly, it's going to depend on where you live geographically what your chances of survival are...
Yeah, where will millions of Bangladeshi's go? And Floridians?
I've read that evidence has been found that a huge Asian lake went dry in Roman times and drought might have sent the "Asian hordes" to Europe. And Syria's problem may be due to drought in eastern Syria causing people tp go to western Syria.
Here is a related article looking at adaptations to climate change.
On a personal level for all of us it won't matter, our genes are set. The results of a climate catastrophe on the human genome won't manifest for 100's to 1,000's of years. My interest lies in the relative near future, 5 to 25 years, the human need for food,water, housing, clothing, community, commerce etc.
I'm all about me and my loved one's first, the rest of humanity comes second.
To answer the OP's question I have no doubt the gene pool would be affected. If the planet goes from 7billion people to 1 billion or less there will be an inevitable loss of gene diversity.
But it all hinges on what Tom S. means by the word "improve".
Sounds like a reason to start handing out life prison sentences for improper genes. Or maybe forced vasectomies and tubules. And labor camps for children over 8 years of age....I think I'm on a roll. :)