Half-Heusler alloys are thermoelectric materials that enable direct conversion of waste heat to electricity. A systematic study of these alloys has never been attempted using local Gaussian type orbitals (GTOs) and hybrid density functional theory methods within a periodic approach. In this work, we study the thermoelectric properties of TiMSn (M = Ni, Pd, and Pt) alloys with space group F4¯ 3m using the CRYSTAL code. We, first, set benchmarks for TiNiSn by comparing our data to existing literature values of Seebeck coefficient, power-factor, and thermoelectric figure-of-merit. Our results agree well. We, then, extend these calculations to TiPdSn and TiPtSn, for which consistent previous data are limited. Our computations show that all TiMSn (M = Ni, Pd, and Pt) alloys prefer p-type carriers and exhibit a figure-of-merit of ≈1 at a chosen carrier concentration and temperature. In addition, we aim to explain the low band-gap of TiNiSn by modeling defects in the pure system. Our defect model proves to have a smaller band-gap, and its power-factor is found to be almost twice of the pure TiNiSn.