The RC82 was developed by Dome for the 1982 racing season. While the design originated with the Japanese firm, the chassis was constructed by March Engineering. The car was initially powered by a 3.3-litre Cosworth DFL V8 engine.
The vehicle made its competitive debut at the 1982 6 Hours of Silverstone. Backed by sponsorship from Amada, the factory team entered a driver lineup consisting of Chris Craft, Raul Boesel, and Eliseo Salazar. The debut ended in retirement after 116 laps due to fuel pressure issues.
The 1982 and 1983 seasons saw the RC82 focused primarily on the 24 Hours of Le Mans. In the 1982 edition, Craft and Salazar returned to drive the car, but were forced to retire after 85 laps when the suspension mounting failed.
The car remained out of competition until the 1983 24 Hours of Le Mans. For this entry, Nick Mason joined the driving squad. The RC82 again failed to reach the finish, retiring after 75 laps following a clutch failure. Following this event, the factory team began phasing out the car in favor of the successor model, the Dome RC83.
In 1984, the RC82 was sold to Dorset Racing. The privateer team entered the car in the 1000 km of Silverstone with drivers Richard Jones, Mark Galvin, and John Williams. The race ended after 46 laps when a valve in the Cosworth DFL engine broke.
Dorset Racing entered the 1984 24 Hours of Le Mans with Nick Faure replacing Williams. This entry marked the car's longest competitive run, completing 156 laps before a drop in oil pressure forced another retirement. Between 1985 and 1986, Dorset Racing lodged entries for the 24 Hours of Le Mans and the 1000 km of Hockenheim with drivers Martin Birrane and Tony Birchenhough, but the team failed to attend these events.
The car was later purchased by Mark Hales, who replaced the original Cosworth powerplant with an 8-litre Chevrolet V8 engine. Hales attempted to enter the car in the 1987 Thundersports series at Oulton Park and Donington Park, but these appearances did not materialize.
The RC82 made its final appearance at a race weekend in 1988 at the Oulton Park round of the Thundersports series. Entered under the Direct Car Phones banner by Hales and co-driver Bill Hall, the 8-litre Chevrolet engine failed, preventing the car from starting the race. A final entry was made for a Thundersports round at Brands Hatch, but the team did not attend, marking the end of the vehicle's racing career.
The Dome RC82's competitive history is defined by its lack of finishes. Throughout its tenure with both the factory Dome team and privateers, the car never completed a race distance. It was superseded by the RC83, which achieved marginally better success than its predecessor.