Sweden's national weather agency SMHI issued expanded a yellow warning previously issued for parts of northern Sweden to cover large areas of both central Norrland and the Norrbotten region.
SMHI predicts that between 35 and 70 millimetres of rain could fall over the course of the day, bringing a risk of flooding.
Drivers are advised to allow more time for their journey and adjust the speed according to road conditions.
"Travel times may increase due to poor visibility and risk of hydroplaning," SMHI warned on its website. "Roads and underpasses may be flooded, avoid driving through the water."
It also warned of flooding in for example basements and stormwater systems.
"Check if you can seal your basement, or move items that are at risk of being damaged by water. Clear gutters, storm drains and other waterways so that the water can flow away unimpeded."
The warning is in place until 7pm on Monday.
Meanwhile, an orange warning for high temperatures remains in place across parts of Blekinge, Kalmar and Kronoberg in the south.
Over the weekend, several Swedish cities saw temperatures climb to unprecedented levels.
Malmö smashed its temperature record after reaching 35.1C, while Lund hit 36.3C as the heatwave peaked on Saturday.
The all-time Swedish heat record remained untouched at 38C (in Målilla in 1947 and Ultuna in 1933).
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.