The vast majority — more than 9000 — were among people aged 65 and above, according to data published by EuroMOMO, a network backed by the European Centre for Disease Prevention and Control and the World Health Organization.
Extreme heat can kill by causing heat stroke, or aggravating cardiovascular and respiratory diseases, with older people among the most vulnerable.
"To have this kind of excess at this time of year is unusual. It’s really high," Lasse Vestergaard, Chief Physician at Denmark's Statens Serum Institut, which hosts EuroMOMO, told Reuters.
"It is difficult to explain this high excess mortality by anything but the extreme heat," Vestergaard added.
Scientists have said the late-June heatwave would have been "virtually impossible" without human-caused climate change, which is making heatwaves more frequent and intense.
The data, pooled from national mortality statistics in 27 European countries, included excess deaths from all causes, not just heat-related ones, during the week of June 22 to 28, when the heatwave peaked in France, Spain, Britain and other countries.
But scientists said there were no other known major factors, such as COVID-19 outbreaks, that would have contributed to the spike to 10,650 excess deaths in that week.
The same European countries' combined mortality over the previous eight weeks was, on average, around 500 deaths per week below typical levels. The EuroMOMO data could be revised in future weeks as more data comes in.
The extreme heatwave at the end of June disrupted power supplies, shut schools, and smashed temperature records in France, Spain and the UK.
EuroMOMO does not publish excess deaths per individual country, but it noted that France and Belgium were the only two countries in Europe to log "very high excess" mortality in the last week of June.
Belgium's excess mortality was the highest during any heatwave in records going back to 2000, according to the country's public health institute Sciensano.
A separate scientific study, published on Monday, estimated 2700 people died from heat-related causes in England and Wales alone, during the May and June heatwaves.
Of those deaths, 42% were caused by the extra heat that global warming contributed to the heatwaves, according to the findings by Imperial College London, the UK Met Office and the London School of Hygiene & Tropical Medicine.
