The extremely cold weather is expected to continue in many areas, reports broadcaster NRK.
Areas without cloud cover are expected to see the lowest temperatures, meteorologist Rafael Escobar Løvdahlt said to NRK.
"It is difficult to say exactly where it will be coldest," Løvdahl said.
The regions that were particularly cold on Sunday night may yet see even colder temperatures if they do not receive cloud cover, according to the report.
Løvdahl said it was currently difficult to predict exactly where the cloud cover would be.
"Tomorrow we will get a somewhat unusual combination of wind and extreme cold over southern Norway, which could result in ships suffering atmospheric icing," he said.
Cold reaching 30 degrees under freezing was recorded in Finnmark, Nordland, Trøndelag and Vestfold, as well as in Hedmark.
Norway's official coldest ever temperature of -51.2°C was recorded in Karasjok in Finmark in 1999.
The northern part of Hedmark, where Sunday's low temperature recorded, has also registered the record lowest temperature for several different years, including -42.4°C in 2010 and -43.9°C in 2001, NRK reports.