In this paper, we report the results of thermal simulations made for the cryogenic target of Laser MegaJoule (LMJ). Thermal simulations are done with FLUENT for a new 3-D model which takes in account the fill tubes of the hohlraum and the membranes geometry inside the hohlraum. Firstly, a 1-D simple analytical model was developed in order to help us to limit the number of simulations and time calculations. Then, with the 3-D model, we have studied the effect of external radiation when shield is disconnected from the cryostat and we have determined the maximal height of shield removal before the shot. Finally, we have studied the sensitivity of the target to thermal contact resistances.