If nothing is done, heatwaves could lead to the deaths of 90,000 Europeans each year by the end of the century, the European Environment Agency said.
"Without adaptation measures, and under a scenario of 3 degrees Celsius global warming by 2100, 90,000 Europeans could die from extreme heat annually," it said.
"With 1.5 degrees C global warming, this is reduced to 30,000 deaths annually."
Countries have pledged to keep global warming to 1.5 degrees Celsius above pre-industrial levels — a goal the world is set to miss on current emission trends.
Some 129,000 Europeans died from excessive heat in the period between 1980 and 2020, the agency said, citing insurance data.
But more frequent heatwaves linked to climate change, an ageing population and increased urbanisation have made this figure likely to increase in coming years, especially in the south of the continent, it said.
The World Health Organisation on Monday said at least 15,000 people had died so far this year in Europe because of hot weather.
The three months from June-August were the hottest in Europe since records began, and the exceptionally high temperatures led to the worst drought the continent has witnessed since the Middle Ages.
Beyond the danger of heat itself, the EEA said, climate change could also make Europe more prone to infectious diseases such as malaria and dengue fever spread by mosquito bites.
And the warming sea waters are becoming increasingly suitable for the bacteria that causes cholera, in particular along the coastlines of the Baltic Sea.
The EEA called for action.
"Nearly all deaths associated with high temperatures are preventable in the European context," it said.