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Ca3Co2O6 is a rare example of one-dimensional Ising spin-chain material with the moments preferentially aligned along the c axis. In this work, we study the c-axis thermal conductivity (κc) of Ca3Co2O6 single crystal at low temperatures down to 0.3 K and in magnetic fields up to 14 T. The zero-field κc(T) shows a large phonon peak and can be well fitted by using the classical Debye model, which indicates that the heat transport is purely phononic. Moreover, the low-T κc(H) isotherms with H || c display a field-independent behavior. These results indicate that there is no contribution of magnetic excitations to the thermal conductivity in Ca3Co2O6, neither carrying heat nor scattering phonons, which can be attributed to the Ising-like spin anisotropy.