In 1983 he drove in the CART Championship Car race at Atlanta Motor Speedway and finished 12th, he then prepared to qualify for the 1983 Indianapolis 500. He spun the car into a wall and shattered his ankle. Between 1983 and 1986 he raced in NASCAR's Winston Cup series. He qualified in the only field in Talladega Superspeedway history in which every car qualified with a speed in excess of 200 miles per hour. He raced in 31 races, with no top-10 finishes. Heveron is best known for flipping over in turn one at the 1984 Firecracker 400, which brought out the final caution to set up an exciting finish with Richard Petty and Cale Yarborough, Petty beat Cale en route to his 200th win. Heveron's best year was 1986, when he finished 35th in points.