Nicola Maxey, spokesperson for the Met Office, said the cool weather will bring the risk of hail and thunder by tomorrow.
But strong winds are still expected and the Highways England warning applies to the whole of the UK.
Winds could touch 60mph along the southwestern coasts through this morning (Monday) with 70mph gales forecast later on Tuesday.
The heaviest areas to be hit will be Belfast and parts of Co Armagh, the Met Office said.
The Met Office has put a yellow warning in place between Tuesday at 8pm and Wednesday at 10am.
A yellow warning means people should "be aware" of severe weather.
Chief forecaster Andy Page warned inclement weather could spark travel disruption over the next three days.More news: Brokers Issue New Targets On Teva Pharmaceutical Industries Limited (NYSE:TEVA)
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Strong winds and stormy weather are set to batter the capital this week.
"There is also a small chance of flooding affecting homes and businesses".
The Met Office said: "Very strong winds with gusts of 55-65 miles per hour, perhaps reaching 75 miles per hour in exposed places, are looking increasingly likely on Tuesday night into Wednesday morning".
A Met Office rain warning said: "30 to 40 mm of rain falling within six to nine hours seems likely to lead to flooding of some sections of road and perhaps also properties".
Damage to trees and perhaps buildings, as well as power cuts are expected, while flying debris and large coastal waves are possible and could cause injuries.
Temperatures are set to dip to around 7C to 9C.