Upon graduation Thunemann was engaged by the North German Radio Symphony Orchestra of Hamburg where he served as principal bassoonist from 1962 to 1978.
On his recordings, he has collaborated with many artists including pianist Alfred Brendel, oboist Heinz Holliger, and the chamber group I Musici.
[1] Thunemann served on the faculties of the Hochschule für Musik, Theater und Medien Hannover, the Hochschule für Musik Hanns Eisler Berlin, Madrid's International Institute of Chamber Music[2] and the Reina Sofía School of Music in Madrid.
[1] Upon his retirement from teaching in Germany, the German government honored Thunemann in 2006 with the Order of Merit of the Federal Republic of Germany (the Federal Cross of Merit, Verdienstorden der Bundesrepublik Deutschland).
In October 2008, he appeared at the Jerusalem International Chamber Music Festival playing the Bassoon Sonata by Saint-Saëns.