Indirect-drive cryogenic target is a main path to realize inertial confinement fusion (ICF). It needs to fill the capsule with a spherically symmetric fuel ice shell. Low mode roughness of the ice layer significantly impacts the hydrodynamic instability in the target implosion. It is determinated mostly by the thermal uniformity of the capsule. Due to the beta-decay heat of tritium, temperature profiles of the targets filled with deuterium-tritium (DT) are different from those filled with deuterium-deuterium (DD). In a cylindrical hohlraum, the DT-filled capsule is always the warmest and forms remarkable radial thermal gradient. The cylindrical geometry makes the capsule equator cooler than the two poles in the steady state if without any intervention. It results in a remarkable second mode asymmetry of the fuel ice layer. Precisely tuning the vertical temperature distribution is essential and full of engineering challenge for a cylindrical cryogenic target of several millimeters. Theoretically, the vertical thermal gradient turning capability demands large thermal resistance of the target thermal mechanical package (TMP). This is contrary for the intrinsic thermal uniformity of the capsule because the larger thermal resistance of TMP results in less thermal smooth of the outside nonuniformity. To reduce the second mode asymmetry of fuel ice, several structural designs, materials with high conductivity (oxygen-free copper) and low conductivity (duralumin) of the TMP are analyzed and compared for the vertical tuning performance. The experiments verify the good tuning efficiency of duralumin TMP but reveal serious ice layer asymmetry around the capsule equator at the same time. To improve the capsule circumferential thermal uniformity with the precondition of good vertical tuning capability, the influence of the asymmetric thermal contact between the cooling arm and the duralumin jacket is analyzed and verified by layering experiments. Finally, the circumferential uniformity is improved by elaborate design of the TMP including the arm-jacket interface and connection band. Under the design optimization, the thermal uniformity of the global surface of the capsule is significantly improved with a reasonable vertical tuning load. It brings a significantly improvement of the DT ice layer quality.