Summary form only given. The paper proposes the modeling and the optimal management of a hot-temperature (Sodium Nickel Chloride) battery system coupled with wind generators connected to a medium voltage grid. A discrete-time model of the storage device reproducing the battery main dynamics (i.e., state of charge, temperature, current, protection, and limitation systems) has been developed. The model has been validated through some experimental tests. An optimal management strategy has been implemented based on a forward dynamic programming algorithm, specifically developed to exploit the energy price arbitrage along the optimization time horizon (“generation shifting”). Taking advantage of this strategy wind generation performances can be enhanced and adapted to load demand, obtaining an increased economic gain measured by the difference between the economic revenue obtained with and without the proposed generation shifting policy.