Heshka played his junior years for the Everett Silvertips of the Western Hockey League. Upon completing his time with the Silvertips, Heshka was signed by the Vancouver Canucks to a three-year entry level contract on July 24, 2006. In his professional debut season in 2006–07, Heshka played with the Canucks affiliates, the Manitoba Moose and the Victoria Salmon Kings. Following two strong and productive seasons with the Moose in the American Hockey League, Heshka's rights were traded by the Canucks to the Phoenix Coyotes at the 2009 NHL Entry Draft on June 27, 2009. On July 3, 2010, Heshka signed a one-year contract to remain with the Coyotes. Shaun was initially assigned to the Coyotes AHL affiliate, the San Antonio Rampage to start the 2009–10 season. After leading the Rampage defence in scoring, Heshka received his first recall from the Coyotes on November 6, 2009. He made his NHL debut the following night, in a tight game with the Anaheim Ducks on November 7. On November 12, Heshka brought home his first career NHL point, an critical assist on a Paul Bissonnette goal, in a 4-2 defeat to the Montreal Canadiens. After 8 games and 2 assists with the Coyotes, he was then reassigned to the Rampage after a number of Coyotes players returned from injuries. Unable to reach an agreement or be traded, the restricted North American was forced to play overseas. He signed with EC Red Bull Salzburg team on September 6, 2010. The 25-year-old remained restricted throughout the 2010–11 season to the Phoenix Coyotes. He went on to play a critical defensive role in the Red Bulls spectacular 2011 season, securing his position as a team leader in the overtime championship win in game 7 of the series final. On November 15, 2012, Heshka signed a two-year contract with Porin Ässät of the Finnish SM-liiga. In the 2012–13 season on April 24, 2013, Heshka won the Finnish Elite League championship with Porin Ässät. He was named to the SM-liiga Allstar team as well as being named the Best Defenseman of the league On June 18, 2013, Heshka departed Ässät on a mutual release and signed a two-year contract with Ak Bars Kazan of the Russian Kontinental Hockey League. He led the team's defence in scoring and was named to the starting line-up of the KHL Allstar Game for Team East held in Bratalsava. In the midst of his second season with the club under a new head coach in 2014–15, Heshka was traded to fellow KHL club, Admiral Vladivostok on October 31, 2014. After playing out the season with Vladivostok, Heshka left the KHL to sign a one-year contract in Sweden with Modo Hockey of the SHL on May 28, 2015.
Personal life
Shaun is married to Laura Heshka, and they reside in Winnipeg, Manitoba in the off season.