Kevin O'Sullivan (59) died in Naas General Hospital on Wednesday after being hit by the car at around 3pm.
Garda believe strong sunlight at the time could have affected visibility.
Mr O'Sullivan, originally from Dodsboro in Lucan but living in St Patrick's Park in Celbridge, Co Kildare, was on point duty.
He was directing traffic and operating a stop-go system on the Maynooth/Rathcoffey Road at Graiguesallagh, near Ladychapel, when he was struck by the car.
The accident took place during drainage works on a straight stretch of road.
Mr O'Sullivan, who had been working for Kildare County Council for 22 years, was struck by a car driven by a 68-year-old man.
The car driver is said to be "devastated" by the incident.
Gardai at Leixlip say that the weather conditions, in particular a very strong sun, were a factor leading to the accident. Their investigations are continuing.
Mr O'Sullivan's family have described him as a "complete gentleman" who "always had a smile on his face".
His niece, Sharon O'Sullivan, paid tribute to him as a "much-loved father and brother".
Mr O'Sullivan is mourned by Liz, his daughter Lorna who he "absolutely idolised", and a wide circle of relations and friends.
Gardai have appealed for witnesses to the incident to contact them.