7 High-throughput calculations can be applied to a large number of compounds, in order to 8 discover new useful materials. In the present work, ternary intermetallic compounds are 9 investigated, to find new potentially interesting materials for thermoelectric applications. The 10 screening of stable non-metallic compounds required for such applications is performed by 11 calculating their electronic structure, using DFT methods. In the first section, the study of the 12 density of states at the Fermi level, of pure elements, binary and ternary compounds, leads to 13 empirically chose the selection criterion to distinguish metals from non-metals. In the second 14 section, the TiNiSi structure-type is used as a case-study application, through the investigation 15 of 570 possible compositions. The screening leads to the selection of 12 possible 16 semiconductors. The Seebeck coefficient and the lattice thermal conductivity of the selected 17 1 Corresponding author: barreteau@icmpe.cnrs.fr 2 compounds are calculated in order to identify the most promising ones. Among them, TiNiSi, 18 TaNiP or HfCoP are shown to be worth a detailed experimental investigation. 19