The layman's question. Is there a maximum temperature that can be reached by air on Earth due to global warming? For example, one that would prevent living organisms from functioning? I read somewhere that with the increase of the sun's brightness by 10%, the average temperature on our planet will be 47 C. This, however, only for about 600 million years. Would global warming enable reaching such a high average temperature?
Is there a limit? Yes and no.
No, there isn't really a maximum temperature anywhere near what we're used to. It's certainly possible to reach an average temperature of 47°C. That may well trigger a runaway greenhouse effect, when all the oceans evaporate. Look at our neighbour Venus. On Venus, the greenhouse effect leads to a surface temperature of 467°C. That's very far away from where we are now on Earth, and we'll most likely not reach that any time soon, but it's probably not theoretically impossible to reach. On Venus, the partial pressure of CO₂ is around 9 MPa. On Earth, it's closer to 40 Pa, a factor of around 200,000 less.
There is, of course, a maximum temperature; we can't reach $\infty$°C. Venus may be close to the upper bound. But at that maximum temperature, life on Earth will be history.
Given what we currently understand about climate, it is not likely that Earth could be triggered into a runaway greenhouse effect, nonetheless arrive there without a push from human industrialization. https://www.technologyreview.com/s/426608/how-likely-is-a-runaway-greenhouse-effect-on-earth/
The surface temperature of the sun is about 5778 Kelvin, which is definitely hot enough to destroy any life on earth. As stated, the temperature on Venus is only about 740 Kelvin, in which it is conceivable that extremophiles could live. So "the maximum" for life on earth is likely somewhere between these two temperatures.