Saturday's temperature in Malmö was the hottest since records began, according to national weather agency SMHI.
Neighbouring Lund, meanwhile, experienced its hottest day since 1947.
In Helsingborg and Jönköping, residents sweltered through the hottest June day ever recorded, with temperatures of 33C and 34.2C respectively.
Malmö smashed its temperature record after reaching 35.1C, while Lund hit 36.3C as the heatwave peaked.
In Växjö the mercury climbed to 34.4C, matching the city's previous all-time heat record set in 1992.
Temperatures remained high even after thunderstorms swept the south and west coast on Sunday, but they are expected to drop this week.
"Along the Småland coast, in particular, daytime temperatures could reach around 25C," SMHI meteorologist Viktor Bergman told TT.
Scientists have shown that recurring heatwaves are a clear marker of global warming, primarily caused by burning coal, oil and gas – and warn they are set to become more frequent, longer and more intense.
The World Health Organization said on Sunday that over 1,300 excess deaths had been recorded in Europe since June 21st in connection with the heatwave roasting much of the continent.
Tens of millions braved a weekend of extreme temperatures in Europe as the heatwave moved eastwards, with some countries announcing rising death tolls and health services warning of saturation.
On Sunday morning, French health officials said there had been around 1,000 more deaths than expected in that country just since Wednesday.
With additional reporting from AFP