We have extended the divide-and-conquer (DC) coupled-cluster with singles and doubles (CCSD) to a fractional occupation number (FON) formalism, denoted as FON-DC-CCSD, using the thermal Wick theorem. The motivation is to address the inconsistency in the treatment of orbital occupations between the DC-based Hartree-Fock and the DC-CCSD methods, which adopt the Fermi distribution function and the step function for orbital occupation, respectively. Numerical applications involving polyene chains and single-walled carbon nanotubes confirm that the proposed FON-DC-CCSD method reduces both energy errors and computational costs compared with the conventional DC-CCSD method.