This is a linkpost for the article Global death rate from rising temperatures projected to surpass the current death rate of all infectious diseases combined, published by Climate Impacts Lab, based on this study.
Bill Gates summarised this as follows:
In other words, by 2060, climate change could be just as deadly as COVID-19, and by 2100 it could be five times as deadly.
From the summary article:
New study from the Climate Impact Lab finds people in poor parts of the world are disproportionately vulnerable to the risk of death associated with increased heat.
...the study projects that climate change’s effect on temperatures could raise global mortality rates by 73 deaths per 100,000 people in 2100 under a continued high emissions scenario, compared to a world with no warming. That level is roughly equal to the current death rate for all infectious diseases—including tuberculosis, HIV/AIDS, malaria, dengue, yellow fever, and diseases transmitted by ticks, mosquitos, and parasites—combined (approximately 74 deaths per 100,000 globally).
As far as I'm aware, this modelling also excludes potential exacerbating effects that climate change has on infectious diseases, e.g through the expansion of tropical regions leading to vastly more deaths from malaria.
This latest modelling could impact conclusions on the relative importance of climate change, e.g. examined here, though some estimates indicate that work to mitigate climate change could be more effective than many global health interventions, depending on our assumptions.