Your planet is already like this from your description.
Let me explain. An Earth-clone with way less water, but everything else the same, will be missing the oceans CO2 reservoir. The 38 Tetratons of CO2 will instead be in the upper atmosphere.
To limit Global Warming to 2 degrees, we have to emit no more than 2.9TetraTons of CO2
You have a global warming hellscape already. You'reYour planet is very very hot, but there aren't the storms that earth would get earth, as there isn't as much evaporation.
I don't know exactly where the weather would be mildest, but it will be cool near the poles. Antarctica has potential to be nice a temperate region.
Your 1000km square is a patch at the south pole. Could be nice, with a nice big lake and such, and then deserts for the rest of the planet where the oceans currently are.
There would be an equivalent temperate zone at the north pole, but with no lake, there will be no evaporation. No evaporation means no rain, so it's just a colder desert.