The temperature distribution within the LMJ target has been extensively studied during the past three years regarding its constitutive materials, its geometry and its thermal environment within the LMJ experiment chamber. By the way, the target definition has evolved and a new architecture is now under consideration. A complete three-dimensional thermal simulation of this prototype has been lead. Its results are described in the paper. At the same time, our calculation efforts were focused on cavity hydrodynamics, especially concerned with overcoming free convection. Previous simulations results have indeed indicated that the thermal distribution is dependent on the filling pressure when the latter is over 10 kPa. Cavity filling CFD simulations are also presented and discussed.