Heyer was born in Mönchengladbach, Germany. His parents ran a bitumen and concrete mixing company. He developed his passion for motor racing during his school years at Adenau, close to the Nürburgring. He later completed an apprenticeship with Daimler-Benz as a mechanic, finishing in 1962.
Living near the Dutch border and unable to race in Germany at 16, Heyer began karting in the Netherlands in 1959. He won the Dutch 100cc kart championship in 1962 and the 125cc class in 1963. Back in Germany, after early difficulties obtaining a racing licence, he competed in the Formula K class from 1965, and claimed both the German and European Formula K titles from 1968 to 1971 in a Taifun/BM. He also competed in the Brignoles 24 Hour Classic in France across 1969–71, winning twice.
Through the 1970s, Heyer became closely associated with Zakspeed, racing their Group 2 Ford Escorts in the European Touring Car Championship, winning the title in 1974, and the Deutsche Rennsport Meisterschaft (DRM), where he was champion in both 1975 and 1976. He made two European Formula Two appearances in 1976, finishing sixth at the Hockenheim opener before failing to qualify for the second race there.
In 1980, Heyer won the DRM again, this time driving a Group 5 Lancia Monte Carlo Turbo for Lancia — a car he also helped develop. A heavy crash at the Norisring in Nuremberg, in which his 480 hp car rolled multiple times, ended his day but not his season. After escaping unhurt, he returned to the wreck to retrieve his famous hat before undergoing a medical examination.
During the years the Spa 24 Hours formed part of the European Touring Car Championship and the inaugural World Touring Car Championship (1982–1988), Heyer won the race three times in succession: in 1982 in a BMW 528i with Armin Hahne and Eddy Joosen; in 1983 in a BMW 635 CSi with Hahne and Thierry Tassin; and in 1984 in a TWR Jaguar XJS alongside Tom Walkinshaw and Win Percy. He also won the 12 Hours of Sebring in 1984, sharing a Porsche 935 with Stefan Johansson and Mauricio de Narvaez.
Heyer retired from racing in 1989, having contested 999 races across 30 years.
Heyer's sole attempt at Formula One produced one of the most unusual entries in the sport's record books. He entered the 1977 German Grand Prix at the Nürburgring with the ATS team — a new German outfit — but failed to qualify, ending up as the third reserve driver. In the event, the two drivers ahead of him on the reserve list were both unable to take their places: Patrick Nève was not prepared to race by Frank Williams, and Emilio de Villota suffered a last-moment engine failure before the start. As the chaos of a first-lap accident consumed the grid, Heyer slipped out of the pits and joined the race.
He ran nine laps before his gearbox failed. Only at that point did officials realise he had been competing without entitlement. He was disqualified and subsequently received a technical ban from five Formula One races — effectively a lifetime ban given that he had no further intention of competing in the series. The episode left Heyer as the only driver in the sport's records to hold a DNQ (did not qualify), DNF (did not finish), and DSQ (disqualified) for the same race.
After retiring from racing, Heyer worked in his family's concrete business. He tested Mercedes-Benz truck racing vehicles between 1990 and 1991, and made several further competitive appearances in the Nürburgring 24 Hours and the Nürburgring 500 km race through the 1990s. In 2004, Volkswagen director Kris Nissen arranged for Heyer to race his milestone 1,000th event in the ADAC Volkswagen Polo Cup at the Norisring, competing against much younger drivers. His son Kenneth Heyer has since competed professionally in GT racing.