Are 60C heat waves predicted by 5C of global heating? (The worst consequence of global heating) It seems to be the case that 1C of global heating caused the whole global temperature bell curve to shift two standard deviations to the right. (see below)

To anyone knowing much about statistics and bell curves this would seem to make the 80 years BAU 5C temperature anomaly have the drastically lethal consequence of much more frequent heat waves greatly exceeding the 44C maximum human survival limit. 

My own projections of the current trend are a little more pessimistic than IPCC RCP8.5 projections. They simply extrapolate the current exponential increase of atmospheric CO2 and project 877 PPM by 2100 then apply the current IPCC equilibrium CO2 sensitivity formula

3C ± 1.5C for every doubling of atmospheric CO2
log2(877/280) * 1.5 = 2.47
log2(877/280) * 3.0 = 4.94   // Business as usual for 80 more years
log2(877/280) * 4.5 = 7.41

​​​​https://www.giss.nasa.gov/research/briefs/hansen_17/ 
When we examine this graph we see that a single degree of temperature anomaly is associated with a shift of the whole temperature bell curve two standard deviations to the right. 



If we hypothesize that a single degree of temperature anomaly directly caused the entire bell curve to shift the right two standard deviations then the consequences of a 5C would seem to be quite lethal. 

Once we numerically quantify the relationship between temperature anomaly and shifts of the bell curve then we would be able to apply this to historical geographical  temperature extremes and predict the frequency, geographic and temporal extent of heat waves that would kill everything within their boundaries. 

This relationship seems to predict that the 5C temperature anomaly projected from "business as usual" for 80 more years could reasonably result in 60C (140F) killer heat waves. A 60C heat wave will kill everything in its path very quickly. Apparently humans cannot survive 44C for very long.
Neither an answer, just common sense.

Not sure if anybody can give exact numbers for temperatures of future heat waves in their projections. Predictions are difficult, especially those regarding the future. But there is consensus and now observation that heatwaves become more frequent and hotter not only on land. One could perform a search for publications that deal with the impact of land heatwaves, e.g. on agriculture (wheat for example), desertification, loss of habitable space, flooding, loss of resources like potable water, etc. There is a lot of published work around.

We went past the 1°C warming compared to pre industrial levels in 2015, after [https://www.ncdc.noaa.gov/cag/global/time-series] and many publications. Current estimations range between 0.9 and 1.6°C for 2019. Several islands have been devastated in the past years, damage still not totally repaired. Jakarta is drowning, catastrophic fires in California, Australia and elsewhere, fed by drought, heat and mismanagement, cost lives and property.

The effect of past and current heatwaves on the health of the population is pretty well visible, western European countrie's and the US health departments have published their estimations of fatalities attributed to heat.