Körting was born in Munich. His parents, Helen and Berthold, operated a workshop in Oranienburg and collaborated with ceramic artist Otto Douglas Hill. At the age of sixteen Heiner-Hans was an intern there and from 1929 to 1931 he studied at the Keramische Fachschule. In 1949, Körting took over the former Bauhaus workshop in Dornburg that had been run by the master potter Otto Lindig. He worked there with his first wife, Gerda Körting (1935–55), and his second wife, Lisa, whom he married in 1955. His son Ulrich still runs the studio and another son, Kristian, is also a ceramic artist, with a workshop in Remschütz near Saalfeld.