I think an ice age and global warming are how the planet controls overpopulation

This is how I think the mechanism actually works.

Too much population of any intelligent species (including humans) creates fire and  internal combustion engines. This creates CO2. This creates the Greenhouse effect over time. This then creates heating the world up to a 76 degree average year around at the north and south pole. By then, anyone who hasn't moved underground during most of the day most places on earth is already dead from the heat. Farming would have to stop unless you used something like grow lights underground because greenhouses would be just too hot over most of the earth (if the average temperature at the north and south poles is 76 degrees Fahrenheit.)

By the way I think a 76 degree Fahrenheit average is much greater than any average in Hawaii during the summer time there (between June and the beginning of September). So, if you want to spend a summer in something close to 76 degrees average try spending a summer in Hawaii without any air conditioning where it might be close to this.

Also, there is no land at the north pole so anyone trying to stay cool there would have to be on board a ship or boat because all ice wouldn't be there most times during the year at that point (or at all).

Only Antarctica has land under it which is going to be very valuable indeed along with northern Canada and Siberia (at least until the next ice age starts) whenever that is.