ICF design requires smooth and uniform deuterium-tritium (D-T) ice layers in a spherical shell. Thermal environment around the capsule is the key to reach the low-mode ice layer roughness requirement and obtain a high quality ice layer. In this paper, we present the results of three-dimensional simulation for an indirect-driven cryogenic target, focusing on the issues of heat transfer and natural convection flow inside the hohlraum. A thermal and hydrodynamic calculation is first proposed to investigate the convection heat transfer effect on the D-T ice layer. Comparing the two cases with gravity considered or neglected, we find that the temperature variation at the ice layer inner surface caused by the natural convection flow and the hohlraum's structure are of the same order of magnitude. Then the parameters study on Rayleigh number, which is a dimensionless number associated with free convection, is carried out. Thermal simulations on different Rayleigh number are provided. Temperature variation at the D-T ice layer inner surface is to increase as soon as the Rayleigh number reaches 60. Comparisons among different gases under different operating pressure conditions are made. In order to avoid the convection heat transfer effect in a wide range of pressure, it is necessary to take pure helium or mixture gas with a small amount of hydrogen as the tamping gas. The influence of hohlraum's orientation on the natural convection is also studied. It is found that the convective heat transfer effect in a horizontally orientated hohlraum is stronger than that in a vertical one. Based on these, we discuss the possibility to eliminate the convection flow by partitioning the hohlraum into several regions. The calculated results for several cases of different gas-region models indicate that the convection flow can be eliminated with an appropriate division in a vertically orientated hohlaum but cannot in a horizontally orientated one. The conclusions in this paper have certain guiding significance for further design and experiments of cryogenic target.