A 2 degree increase in temperature due to climate change does not seem so bad, if you live in a cold country, or if you recall that temperatures increase and decrease by a lot more that that on a daily or seasonal basis. However, a 2 degree increase is serious for many reasons. One of them is the wet bulb temperature.
The wet-bulb temperature is the temperature read by a thermometer covered in water-soaked cloth. At 100% humidity the wet-bulb temperature is equal to the air temperature (or dry bulb, or normal temperature).
At lower humidity the wet-bulb temperature is lower than dry-bulb temperature. E.g. at 35C with very low humidity the wet bulb temperature would be lower than 35C.
Normally sweat evaporating takes heat away from our bodies. However at a wet bulb temperature of about 35 degrees (it is not precise) the human body cannot radiate away heat, and the sweat just clings to your skin, and so your body cooks itself until you die, even if you are a young, healthy adult in the shade. This would take a matter of hours once the temperature is reached.
A wet bulb temperature of 35 degrees could be 35C at 100% humidity (in theory, but I don´t think 100% humidity is common), 40C at 70% humidity, 45C at 50% humidity or 50C at 35% humidity. Each is the same on the scale of wet bulb temperature, and all are similarly deadly. https://www.omnicalculator.com/physics/wet-bulb
I would guess that the cases of 40C at 70% humidity or 45C at 50% humidity are probably the most likely combinations for a mass death event since 100% humidity and 50C are both uncommon in habited areas.
At the moment, it is very rare to have a wet bulb temperature that is high enough to be deadly for young healthy adults. But climate change may change this.
The world has heated 1.2C. However, that temperature is the average for the globe. In the oceans, it has heated about 1.0C so far, while on land it has been nearer 1.7C. That should reach 2.0C on land by about 2030 or 2040.
A 2C addition to the worst heat waves should not be a major problem if you are a young healthy adult and live in a cool place such as the north of Europe, US, or Japan and stay indoors or in the shade in the worst heat.
However in some places of the world, including India, Pakistan, the Middle East and Africa, indeed much of the humid tropics, this could be a major problem. That 2C could make the difference between the human body being able to radiate away heat and not. It could make the difference between a heat wave that kills hundreds and a heat wave that kills thousands or millions.
The recent heatwave in India in Pakistan was not a mass death event because the humidity in April and May is lower: https://en.wikipedia.org/wiki/Climate_of_Delhi. However >40C temperatures in June or July could be a different matter.
When the wet bulb temperature is reached, some options to save yourself might include going to a building with air conditioning (if you can access one) or getting in a vehicle and going to the coast or the mountains (if you can and if they aren´t too far). However, it´s quite possible that some people will not want to miss a day´s work and lose pay, so would still work on very dangerous days.
One possible problem is that electrical grid failures are likely to be higher in an extreme heat wave, as record temperatures stress cables, infrastructure and power stations while the use of electricity rises due to increased air conditioning. This could cause power blackouts which could lead to mass deaths due to the lack of air conditioning.
It´s also worth remembering that climate change causes many effects that can happen together. For example, a wet bulb event may happen in the future at the same time as a drought, famine or war caused by climate change.
It looks like above or below 2.0C might make a big difference in terms of mass deaths and habitability of large parts of the globe. Yet another reason to add to the huge list of arguments to use less fossil fuels like petrol, diesel, gas, coal etc.
Videos of 10 minutes or less on Wet Bulb Temperature:
https://www.youtube.com/watch?v=EIJeJcLun7Y (basics)
https://www.youtube.com/watch?v=65i8YREVW54 (effects globally)
https://www.youtube.com/watch?v=m8Af-mbKCB0 (extra one if you´re really keen)
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