The thermovoltages in the case of a nonlinear absolute Seebeck‐coefficient S(T) of a material A are discussed up to the quadratic term in the expansion of S(T) for inhomogeneous (AB) as well as for homogeneous (AA) material rings. The quadratic term results in additional thermovoltages and in particular in a Benedicks effect, ΔuAA ∼ (ΔT)3, but only if there is a thermal asymmetry in the bisectional ring AA, too. The coefficients of the expansion of S(T) are calculated for the case that the quadratic term originates from the thermal expansion of a metallic material, using the Boltzmann–Fermi theory.