Born in Ochsenwerder, Heitmann's first training in organ playing was with his father, who was also an organist.
From 1909, he was at the University of Music and Theatre Leipzig a student of Karl Straube, Max Reger and Josef Pembaur.
In 1918, Kaiser Wilhelm II, German Emperor appointed him organist at the Kaiser-Wilhelm-Gedächtniskirche in Berlin.
From 1923, Heitmann taught at the Berlin Academy for School and Church Music, where he was appointed professor in 1925.
Shortly before the end of the Second World War, he was included in the Gottbegnadeten list compiled by Joseph Goebbels as one of two organists.