The Cooling of Low Enriched Uranium (LEU) irradiated fuel plate targets that used for Molybdenum -99 productions, after their extraction from the nuclear reactor core require a good degree of interest. This is to satisfy two important criteria's, the first keeping the radiation dose limits within the safety limits to protect the worker and the second to keep the integrity of the plate itself for easy handling and manoeuvring at the different stages. The cooling processes of the plate targets are passing through different modes, by forced convection cooling using water coolant inside the core during irradiation, by natural convection cooling using water coolant inside the reactor main tank during the decay period and finally by air convective and radiation inside the hot cell during their loading. In this study, a steady state mathematical model was developed to study the effect of thermal contact resistance and the ambient air temperature inside the hot cell on plate targets cooling by free convection during an abnormal condition of lose of electrical power supply, which means no ventilation system, is available. In this simulation, it assumed that three targets were unloaded on the table inside the cell in the form of pile, one target on the top of the other, as a purposed human error. The maximum pile temperature variation with target power ratio (target power in hot cell relative to target maximum power during irradiation) was analyzed and calculated. Also the probable temperature variation against different power ratios for one free vertical plate target hold by the Tele-manipulator, exposed to air free convection and thermal radiation on its both sides, during the loading process was estimated in this study. This study was clarified that, the contact resistance and the ambient temperature have an essential effects on the targets plate cooling inside the hot cell as will be clarified in that work.