Claudia Hempel finished sixth and seventh in the 100 and 200 metre freestyles, respectively, at the 1976 Montréal Olympics. She won a silver medal with the East German 4x100 freestyle relay team. She was also on the squads of the 4x100 freestyle and the 4x100 medley relays at the 1975 Cali Worlds, which won gold medals, but with the medley relay she only swam in the heats. In 1975, she had won both distances in the backstroke events at the East German nationals.
Hempel later studied sports and became a sport school teacher, teaching sports and German. Her husband Dr. Hartmut Thamke was a physician and became the club doctor of the football (soccer) club FC Energie Cottbus.