It's not the absolute temperature that is the problem, is the change in temperature. Humans can survive in a pretty large range of temperatures. But the places we currently settle and use for agriculture might become unsuitable. Similarly, the biosphere as a whole can adapt to essentially any temperature; Earth has been significantly hotter than today in the (distant) past. However during times of rapid climate change mass extinctions happen. To my knowledge, temperature hasn't changed as quickly as it is changing today, ever.
It's pretty hard to say how long they usually take because the fossil record from millions of years ago is difficult to date with good accuracy. For example, I don't think we can say with good confidence whether the asteroid that hit us 66 million years ago killed a large fraction of all living creatures within a year, or whether it took thousands of years or longer.
The sources in the Wikipedia article seem to disagree with you on that. Perhaps you want to add your sources to the article and reword it with less strong language.
