|Heat is not the problem.|
But an obvious weakness is point 3. After all, the “Medieval warm period” seems to have been a time of relative prosperity.
Basically, CO2 is food for plants. It is a powerful fertilizer. Therefore, the rising CO2 concentrations that supposedly cause global warming are also certainly boosting crop yields and greening the planet. This may be considered separate from the global warming issue; but any plan to reduce CO2 emissions is also, automatically, going to reduce plant growth (and hence animal habitat) worldwide. Isn't this what we were claiming to avoid?
In general, heat from the sun is also a powerful fertilizer. There is a reason why it is called the “greenhouse effect.” A longer growing season in the temperate zones also means more vegetation and more food.
Is there a tradeoff, conversely, in the tropics? No—even at the equator, it is not “too hot” for agriculture. Flora and fauna are simply much more abundant, and crops come in year-round.
Ah, you are thinking deserts, perhaps? Look on a map. Deserts do not occur at the equator. They are not caused by excessive heat from the sun. They are caused by a lack of moisture, caused in turn by prevailing wind patterns.
So, would global warming increase the size of deserts? Warming, per se, will not, so we have to guess at collateral effects. I ain't no climate scientist, but it seems to me the effect of CO2 promoting plant growth will work to reduce, not expand desert areas. And increased heat should lead to increased evaporation, therefore increased cloud cover, and increased precipitation. Result: less desert worldwide.
However, the bad news is that recent data seem to refute climate change point 1—the Earth has not gotten warmer since the 1990s.