High-temperature thermopower is interpreted as entropy that a carrier carries. Owing to spin and orbital degrees of freedom, a transition-metal perovskite exhibits large thermopower at high temperatures. In this paper, we revisit the high-temperature thermopower in the perovskites to shed light on the degrees of freedom. Thus, we theoretically derive an expression of thermopower in one-dimensional octahedral-${MX}_{6}$-cluster chain using linear-response theory and electronic structure calculation of the chain based on the tight-binding approximation. The derived expression of the thermopower is consistent with the extended Heikes formula and well reproduces experimental data of several perovskite oxides at high temperatures. In this expression, a degeneracy of many-electron states in an octahedral ligand field (which is characterized by the multiplet term) appears instead of the spin and orbital degeneracies. Complementarity in between our expression and the extended Heikes formula is discussed.