A study is conducted on cooling and controlling the thickness of a frozen layer of deuterium and tritium (D-T) on the inner surface of a capsule mounted in a cylindrical hohlraum. Cooling is required to remove the heat released during tritium decay. The layer thickness must be uniform, which requires that the heat flow from the layer into the capsule wall be spherically symmetric. It is shown that this requirement can be satisfied by controlling the temperature rise along the hohlraum wall from the ends to the midplane. The optimum temperature rise depends primarily on the D-T fuel charge and the thermal conductivity of the gas filling the hohlraum. To ensure a layer thickness variation of less than ±0.4 m in a plastic capsule, the temperature rise along the hohlraum wall must be controlled to an accuracy of about ±3.0 mK. However, as the thermal conductivity of the capsule wall increases to metallic material values, the required accuracy of the hohlraum wall temperature rise decreases to ±15 mK.