Born near Charleston Lake, Ontario, Thibeault first played senior ice hockey for the Cornwall Flyers of the Ottawa City League in 1936–37, before moving to the Hull Volants of the Ottawa District senior league for 1937–38 and 1938–39. He left the Volants in the 1938–39 season to turn professional, joining the Springfield Indians of the International-American Hockey League. In 1941, he returned to the Cornwall Flyers, now playing in the Quebec Senior League, for one season. He joined the Canadian Army and played for the Cornwall Army team in the Quebec league for a season.
In 1943, Thibeault signed with the Buffalo Bisons of the American Hockey League (AHL). He had an excellent season contributing 63 points in 51 games. Buffalo traded him to the Detroit Red Wings in 1944. He managed to get into four games with Detroit, getting two assists but played most of the season with the Indianapolis Capitals of the AHL scoring 18 points in 31 games. In 1945, he was traded back to Buffalo by Detroit. In October 1945, Buffalo loaned him to the Montreal Canadiens in exchange for the loan of Wilf Field, Kenny Mosdell and Frank Eddolls. He played one game with Montreal but was returned to Buffalo in November 1945. Thibeault was reinstated as an amateur and returned to the Hull Volants where he played the balance of the 1945–46 season and six games of the 1946–47 season.
Thibeault was moved to the Victoriaville Tigre in 1946 and scored 35 goals and 62 points in the 1946–47 season. His season attracted the attention of the Houston Huskies who convinced him to return to the pro ranks for the 1947–48 season. He scored 12 goals and 29 points in 46 games for the Huskies. During the 1948–49 season, Thibeault split his season with Houston and the San Diego Skyhawks of the Pacific Coast League. He played his final professional season in 1949–50 with the Victoria Cougars of the PCHL, scoring 20 goals and 48 points in 66 games.

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