Andrew Fisher, from Wallsend in Tyne and Wear, died in hospital after the incident on the A75 near the Dromore roundabout in the south of Scotland at around 9am on Saturday.
The 42-year-old was reported to have been taken unwell in the car.
He was travelling in a white Hyundai with a woman and three children at the time, but they were not injured.
Sergeant Leigh McCulloch said: “Enquiries are ongoing to establish exactly what happened and we are appealing to anyone who may have witnessed the incident.
“You may have seen the vehicle, a white Hyundai, driving on the A75 previous to the incident and have dash-cam footage that can help us.
“We ask that you come forward and contact us with any information.”