We analyze the effect of a dissipative bosonic environment on the Landau-Zener-Stuckelberg-Majorana (LZSM) level crossing model by using a microscopic approach to derive the relevant master equation. For an environment at zero temperature and weak dissipation our microscopic approach confirms the independence of the survival probability on the decay rate that has been predicted earlier by the simple phenomenological LZSM model. For strong decay the microscopic approach predicts a notable increase of the survival probability, which signals dynamical decoupling of the initial state. Unlike the phenomenological model our approach makes it possible to study the dependence of the system dynamics on the temperature of the environment. In the limit of very high temperature we find that the dynamics is characterized by a very strong dynamical decoupling of the initial state - temperature-induced quantum Zeno effect.
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