sure it will , it does it every year winter / summer.
20 C is only 68 F and there are plenty of places where temperatures fluctuate much greater than that.
it would probably take several thousands of years to raise the earths ground temperature 68 F anyway.
the earth will still be turning around and cooling the earth during the night.
those who stay on the surface would mostly be dead along with most life on the surface of the earth after only a few degrees temperature rise anyway , the only ones that will survive would be the ones that can live and grow food underground.
lets put it this way you would stand a much better chance of survival below ground than above.
this is why the rich and governments are building large bases underground that have the ability to produce food.
they might act stupid , but they got your vote didnt they.
