Hydrogen permeation is investigated in a conjugated system of Li15.8Pb84.2 eutectic alloy or Ar under natural convection inside a cylindrical vertical sus316 tube. Two different temperature conditions are made between the upper and lower parts of the vertical tube. When thermal convection in Pb-Li or Ar with inside temperature distribution is fast, the rate-determining step for overall permeation rate is considered H2 permeation through the sus316 tube wall maintained at the lower temperature. On the contrary, when the inside convection is slow, the convection affects the transient behavior of overall H2 permeation rates. The analytical result was consistent with experimental ones of the Ar convection system. However, the steady-state overall H2 permeation rate for the Pb-Li system was much higher than the value estimated from the intrinsic permeability of sus316, and the values changed gradually with elapsed time. This may be because hydrogen is present as an atomic state in the Li17Pb83 convection layer with different temperatures, and bubbles on interfaces affect permeation. The overall H2 permeation rates under various temperature conditions are compared, and the effect of thermal convection is discussed.