Novel high-performance materials are needed for developing thermoelectric devices. One way to answer this need is to screen a large number of compounds by first-principles calculations and to synthesize the most promising compounds. We focus our investigation on the ternary intermetallic compounds T-M-X, with T a transition metal, a rare earth or an alkaline earth metal, M an element from the first line of the transition metal and X, a metalloid. For each prototype, all the possible T-M-X combinations are investigated by DFT calculations. Among all these candidates, those which are predicted as thermodynamically unstable and metallic are dismissed. For the most promising compounds, predicted as stable and semiconductor, complementary calculations as the phonon band structure and additional BoltzTrap electronic transport calculations are carried out to better assess their thermoelectric properties. After those theoretical steps, experimental investigations are performed to confirm calculations. The study of the equimolar TMX in four different prototypes lead to the investigation of 2280 possible configurations. Then our screening process allowed us to highlight more than 45 possible new semiconductors. Among these, new compositions such as HfCoP, SrCuSb or TaFeSb were predicted to be stable and non-metallic. Complementary calculations allowed to estimate their lattice thermal conductivity and Seebeck coefficient.