The TPCONT computer code is used to study the thermal-hydraulic behavior of a pressurized water reactor containment after a core-melt accident. A commercial-sized reactor of 1500-MW(electric) power output is especially designed to withstand transient and long-term loads with purely passive means. It is shown that the decay heat can be removed with an optimized cooling system based on natural-convective air flow in the annular gap with sufficient safety margins of maximum pressure and temperature to failure values. Three gap designs, which are different in the treatment of leakage flow, are investigated. In extensive parameter studies, the thermal-hydraulic evolution in the containment is found to be rather sensitive to various system data. Therefore, precise predictions of maximum loads need accurate knowledge of the design data of the reactor under consideration and better physical data, especially concerning heat transfer and flow data in the cooling duct. Various parameters are identified that may be exploited in a careful and optimized design to effectively limit the long-term loads to acceptable values.