Iron Aluminide Fe₂Al₅ has a rigid framework of both fully occupied aluminum and iron sites and channels of partially occupied aluminum sites. On the other hand, Fe₄Al₁₃ possesses a large unit cell with 102 atoms. These complex and peculiar crystal structures bring a low phonon thermal conductivity. Here, we report the thermoelectric properties and discuss how the proposed chain structure and large unit cell can lead to a low phonon thermal conductivity. The calculated room-temperature phonon thermal conductivity by using the Wiedemann-Franz law is approximately 1.5 W/mK and 0.8 W/mK for Fe₂Al₅ and Fe₄Al₁₃, respectively. From the comparison with other Fe-Al alloys, which have neither plural partially occupied sites nor a large unit cell, we found that (1) the specific heat does not decrease at high temperature, i.e. aluminum atoms at partially occupied sites seem to be fixed rather than liquid behavior. (2) the speed of sound for Fe₂Al₅ and Fe₄Al₁₃ are almost identical among Fe-Al alloys, i.e. the average phonon group velocity of acoustic modes for Fe₂Al₅ and Fe₄Al₁₃ are not slower than that of Fe-Al alloys, (3) the electrical conductivities of Fe₂Al₅ and Fe₄Al₁₃ are lower than those of the other Fe-Al alloys. These results suggest that the low phonon thermal and electrical conductivities are brought by short relaxation times of both phonons and electrons due to chemical disorder such as the partially occupied sites.