Mühlmann subsequently studied anthropology, ethnology and sociology at the universities of Freiburg, Munich, Hamburg and Berlin.
Eugen Fischer, Edmund Husserl, Fritz Lenz, Siegfried Passarge, Walter Scheidt [de] and Richard Thurnwald.
Having joined the Nazi Party, Mühlmann completed his habilitation at the Kaiser Wilhelm Society in 1938.
From 1937 to 1943, Mühlmann was editor of the journal Archiv für Anthropologie und Völkerforschung.
At the end of World War II, Mühlmann fled from Berlin to Wiesbaden with his wife.