De Heer debuted his pro career in the Eredivisie with the Tilburg Trappers in 1971-72. He clearly established himself as a force to reckon with that season, with 21 goals and 30 assists in only 17 games. His best season came in 1974-75, where he totalled 120 points in 29 games (61 goals and 59 assists). He left Tilburg in 1976-77 to join the Heerenveen Flyers. He left the team in 1980 after four solid seasons to join EHC Arosa of the Swiss Nationalliga A, with whom he won one Swiss Championship in 1982. Following this championship, de Heer returned to Heerenveen to finish his career.
De Heer represented the Netherlands at several international competitions, including the 1980 Olympics, the only time the Dutch National Team has made it to the Olympics in ice hockey. He finished the olympic tournament with 3 goals and 3 assists; all three goals came as a hat trick against the Polish National Team on February 18th 1980. He retired as the Dutch National Team's all-time leading scorer, with 114 total career goals and 96 assists in 119 games.
- Top scorer of the 1978 World Championship C (14 goals and 17 assists in 10 games)
- Best forward of the 1978 World Championship C
- Top scorer 1980 World Championship B (9 goals and 8 assists in 6 games)