We present a detailed theoretical study of the SnS compound, which has not been investigated in depth to date, concerning its crystal structure, electronic structure and thermoelectric property. The results of this study show that pure SnS is not a good thermoelectric material but that its ZT can be increased by adjusting both the temperature and carrier concentration. Further, the optimal temperatures and carrier concentrations for producing the peak ZT are identified. The peak ZT is always below unity in the low-temperature Pnma phase; conversely, when the crystal undergoes a displacive phase transition at 878 K, the peak ZT is enhanced to 1.61 ± 0.02 at 1080 K. Additionally, the average ZT in the Cmcm phase (e.g., approximately 1.3) is significantly higher than that in the Pnma phase (e.g., 0.31 ± 0.05). Therefore, the optimally doped SnS material may be highly efficient in its thermal-to-electrical energy conversion at high temperatures. We attribute the remarkable high ZT of doped SnS to the high sensitivity of the electrical conductivity to the carrier concentration. The results of this study describe a simple and viable strategy to optimize the ZT value of the SnS compound using the synergetic tuning of temperature and carrier concentration.