Some frost and icy patches might remain on untreated surfaces this morning, the forecaster has said.
There is a chance of a few showers in the western counties, however many parts of the country will remain dry and enjoy sunny spells.
In the north the UK’s Met Office has issued a status Yellow ice warning for all six counties until 9.30am this morning.
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Meanwhile, showers might become more widespread this afternoon and evening, with some of them turning heavy and prolonged, with possible hail.
Temperatures will range between 5 and 9 degrees, as Monday will become windier with winds turning from light and moderate to moderate to fresh and gusty by afternoon.
The strongest winds can be expected at times in the west and northwest.
Monday night will see some showers with long clear spells developing.
Some mist and fog are likely overnight, as temperatures will drop below freezing and will range between -1 to +3 degrees, with light winds.
Cold temperatures will bring patchy frost and ice developing overnight.
Meanwhile, clouds will thicken in the south towards dawn, and the rain will move in across Munster.
On Tuesday, clouds and rain in the south will continue to spread northwards across the country, and some of them might turn heavy.
Temperatures of 6 and 8 degrees are expected in the afternoon, while the southwest and the southern coast will enjoy milder conditions with temperatures ranging between 9 and 12 degrees.
Tuesday night will be wet with rain, which might become heavy in some parts.
The south might be breezy with moderate to fresh and gusty winds.
Tuesday night will see a rise in temperatures, as the south can expect 8 to 10 degrees, while the north will see lows of 4 and 7 degrees.
Met Éireann forecasts an unsettled week with rain and showers at times.