W.De Roeck, C.Maes Steady state fluctuations of the dissipated heat for a quantum stochastic model (70K, latex) ABSTRACT. We introduce a quantum stochastic dynamics for heat conduction. A multi-level subsystem is coupled to reservoirs at different temperatures. Energy quanta are detected in the reservoirs allowing the study of steady state fluctuations of the entropy production. Our main result states a symmetry in its large deviation rate function.