Met Éireann has issued two separate weather warnings for several areas.
A status yellow rainfall warning is in place for Carlow, Kilkenny, Wexford, Cork, Kerry, Limerick, Tipperary and Waterford.
The forecaster says between 30 and 50 mm of rain is set to fall in the 24-hour period from Thursday afternoon to Friday.
It says there will be rain in many areas with a risk of flooding.
A status yellow low temperature warning has also been issued for the entire country overnight.
Temperatures will fall to -3° or -4° in many areas on Wednesday night.
This alert is in place until 9.00am Thursday morning.
Thursday will start off dry and bright with sunny spells and with frost gradually clearing.
In the afternoon, rain will develop in the southwest and will spread across Munster and Connacht in the evening.
Highest temperatures of 9 or 10°, with southeast winds gradually increasing.