I'm finding numbers ranging from 16k (Imperial College London) up to 175k (WHO). All studies I encountered seem to be based on a statistical correlation between heath and death counts, which makes sense as 'heath' is rarely registered as an official cause of death.
Would installing more airco's help? Perhaps, especially some of the poorer regions in the south, hardest hit by climate change, may still have some nursery homes without proper cooling.
But installing airco's isn't even listed in the 4 points of advice provided by the WHO. It's about adapting lifestyles and work practices (think: construction workers) to the changing climate.
The US is not exempt from this. The NY times is reporting a doubling of heath related deaths in recent years, though I can only find numbers based on official causes of death, which cannot be compared to the European numbers.
So no, I don't think this is a great example of all of Europe being too stupid to do even simple things in its own interests.