The risk posed by relatively slight increases in atmospheric temperature, is high.
A wet-bulb temperature (WBT) of 35°C is the theoretical human survivability limit. This recently occured for six consecutive hours in July. Such conditions prevent evaporative cooling, rendering outdoor exposure potentially fatal without artificial cooling. Above 35 wbt, even lying down in the shade is fatal.
All biological systems have a range, and beyond that range the chemistry of life ceases. A body designed to operate with a core temp of 37C, can briefly sacrifice optimal performance to inhibit pathogen replication at 40c (fever), but will start failing, including seizures, at core temp of 41 or 42 c.
If we get prolonged wbt over 35deg, the only humans that survive, will be those in A/C or underground.