Thiessen, in his debut at Canadian Juniors, lost the final of the 2001 Canadian Junior Curling Championships playing lead for Mike McEwen. Thiessen was a member of the 2003 Winter Universiade championship team. He represented Brandon University, playing lead for Mike McEwen. After university, he played lead for Sean Grassie before moving to play in Alberta as Mark Johnson's lead in 2004. In 2006, he moved to play for Kevin Koe. Thiessen won the 2008 Canada Cup of Curling with the team, and qualified for his first Brier in 2010 as Team Alberta. The team won the Brier after beating Ontario's Glenn Howard 6-5 in the final. They went on to win at that year's world championship, securing the gold medal after a win over Norway, skipped by Torger Nergård. After Pat Simmons signed on with the team, they went to their second Brier in 2012, but lost to Ontario, skipped by Glenn Howard in the final. At the 2014 Brier the rink repeated as Canadian champions, defeating John Morris' B.C. rink 10-5 in the final. The team would go on to finish in 4th place at the 2014 World Men's Curling Championship. After the season, Koe left the team and was replaced by John Morris. The team would represent Team Canada at the 2015 Tim Hortons Brier as defending champions. They would win the 2015 Brier and go on to win a bronze medal at the 2015 Ford World Men's Curling Championship. The team would represent Team Canada at the 2016 Tim Hortons Brier for the final time, finishing in 5th place. The team would go their separate ways after the season.