Eight flood alerts are in place across Scotland.
Greg Dewhurst, meteorologist for the national weather service, said temperatures will be milder across the country, but there will be a north-south split in conditions.
He told the PA news agency that the most dramatic change in weather will be in Northern Ireland, Scotland and the far north-west of England.
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“Cloudy and patchy rain are moving in from the Atlantic and winds will turn south-westerly, bringing in milder air,” Mr Dewhurst said.
Temperatures are set to be well above freezing and will rise overnight into Monday, reaching as high as 10C in Scotland.
On Monday, Northern Ireland, Scotland and northern parts of England will be cloudy with outbreaks of patchy rain and temperatures between 9C and 12C.
Temperatures plummeted to minus 18.9C on Saturday morning in Altnaharra, Scotland, and it was the UK’s coldest January temperature in 15 years.
The average low in northern Scotland for this time of year is about 0.3C, while for England, overnight lows are about 1.5C to 1.6C.