The effects of natural convection in the tamping gas in a vertical hohlraum on the heat flow from a frozen layer of deuterium and tritium (D-T) on the inner surface of a target capsule is investigated numerically. The energy released from tritium decay within the capsule is transferred through the tamping gas to the cooling rings on each end of the hohlraum. The thickness of the frozen layer must be uniform. This means that the heat flow from it to the capsule must be spherically symmetric and that the temperature of the inner surface of the D-T layer will be uniform and in equilibrium with its vapor. The objective of this study was to determine the combination of boundary conditions and thin films for restricting convection in the tamping gas, which satisfy these requirements. With the capsule mounted between two thin plastic films, clockwise-flow convection cells form in the upper and lower gas regions. When this flow contacts the capsule, the temperature variation along the inner surface of the D-T layer was as great as 3 mK. This was reduced to 180 K by introducing thin films to isolate the capsule from the convection cells. Further reduction of this value to ~50 K was achieved by modifying the boundary conditions.