 Thiessen is the recipient of numerous awards, including the Governor General's Award for English-language drama ("Einstein's Gift"), the Carol Bolt Award for Best Play ("Vimy") and the Sterling Award for Outstanding New Play ("Apple").He has also received the City of Edmonton Arts Achievement Award and the Alumni Award of Excellence from the University of Alberta.He has been nominated several times for other awards including the Siminovitch Prize in Theatre, and was a finalist for the Governor General's Award for "Lenin's Embalmers".