As far as CO2 goes... it has been multiple times greater in previous time periods with none of the predicted end of the world scenarios taking place. The truly scary threat to life on this planet occurs not in warm times with abundant CO2 but during cold periods when CO2 has been depleted to the point where it has threatened the health of plant life.
For North America certainly. The global data from the 30's is very poor. But the summer heat records from the 1930's still stand for much of the US and Canada.
However one often overlook fact is that there also cold records from the 1930's. Some summers were hot but some winters were cold.
For earlier periods you are correct. There is no way that Greenland can have farming for centuries while the rest of the world is colder. There is simply no pattern than can create that effect for more than a short period, a few years at most. Greenland temperatures for the Medieval warming, Roman warming and prior warming are a valid proxy for global temperatures.