Thompson made his NASCAR Grand National debut in 1950 and demonstrated early promise, winning two of the seven races he entered in 1953 while driving the No. 46 Buckshot Morris Oldsmobile. One of those victories came in the Wilkes 160.
His most productive seasons came in 1956 and 1957, when he was part of Carl Kiekhaefer's powerful factory-backed operation running Chryslers and Dodges. In 1956, competing in forty-two races, Thompson won eight times and finished third in the championship standings. He repeated the third-place points result in 1957 after switching to Chevrolets with Hugh Babb and his own equipment, though his win total dropped to two. He again finished third in 1958 in his own Chevrolet, taking four victories from thirty-eight starts.
A notable achievement came in 1957 when Thompson set the five-hundred-mile speed record for stock cars with an average speed of 100.1 mph — a record that stood only briefly as the sport's pace continued to accelerate. In 1959 he joined the "Pure Record Club" alongside Fireball Roberts, Elmo Langley, and Richard Petty, a distinction given to drivers who had set the fastest qualifying speed in each make of automobile competing. His 1959 season brought another third-place championship finish despite producing no wins from twenty-nine starts, a reflection of both his consistency and the intense competition of the era.
After 1959, Thompson stepped back from the full-time Grand National schedule and shifted his focus primarily to late model racing at local North Carolina short tracks. His final appearance in the top series came in 1971 when he returned for the World 600, finishing sixteenth.
Thompson died on April 2, 1972 — one day before his forty-sixth birthday — during a late model race at Metrolina Fairgrounds in Charlotte. On the twenty-first lap he suffered a seizure, causing his car to crash into a rail. He was pronounced dead on arrival at the hospital. The medical examiner attributed his death to an acute coronary occlusion.
Thompson was inducted into the National Motorsports Press Association's Hall of Fame and the Georgia Automobile Racing Hall of Fame in recognition of his career achievements.
Speedy Thompson's career spanned the critical transitional period in which NASCAR grew from a regional phenomenon into an organized national series with manufacturer backing. His three consecutive third-place championship finishes from 1956 to 1958 demonstrate that he was among the genuine elite of the sport during its factory racing era, even if the dominant machinery of Lee Petty and later the Holman-Moody Fords ultimately prevented him from claiming a title. His twenty career victories place him among the notable winners of the Grand National era.