SMHI is warning that the heat could pose an increased risk of health problems for vulnerable groups if the warm weather persists for several days.
"A high-pressure system and warmer air are moving in. It's not impossible that temperatures will reach 30C in several places," SMHI meteorologist Linus Falk told the TT newswire.
This applies primarily to Wednesday and Thursday, when the heatwave is expected to peak. Temperatures could reach between 26C and 33C as far north as the central Norrland coast.
It is still too early to say whether Sweden will experience "tropical nights" – when temperatures do not drop below 20C.
Despite a previous heatwave in June, the upcoming temperatures are not normal for July.
"It might not completely shatter records, but it is not normal," Falk said.
Meanwhile, the risk of wildfires over the coming days is high in nearly half of the country, and extremely high in certain parts.
SMHI notes that the risk of fires in forests and fields is high in Götaland, Svealand and parts of southern Norrland. In some areas, the risk is very high, and around Bohuslän, Karlstad and Blekinge, it is deemed extremely high.
"It will be very dry and sunny in the coming week. So until the end of the week, people will need to be careful in large parts of the country," SMHI meteorologist Magnus Joelsson told TT.
Local showers could temporarily dampen the fire risk.
"You have to be careful with anything that can start a fire, such as working with machinery. It's well worth checking if there is a local fire ban in place," said Joelsson, adding that the same applies regardless of the risk level.
The dry weather had already made its mark on Sunday. Helicopters water-bombed a forest fire outside Hultsfred and another south of Boxholm, among others. Both fires were estimated to be around two hectares in size.