In this work, we employ density functional theory (DFT) calculations to systematically investigate the thermal and electronic transport properties as well as the thermoelectric performance of antiperovskite (APV) compounds within the Ca3XN family, where X = P, As, Sb, and Bi. Here, post calculations are performed based on self-consistent phonon (SCP) theory and the Boltzmann transport equation (BTE), specifically accounting for four-phonon scattering processes. Interestingly, these materials display notably low lattice thermal conductivity (kappa(L)), approximately 1.1 W m(-1) K-1 at 900 K. As a result, both Ca3AsN and Ca3SbN exhibit remarkably high figure of merit (ZT) values at elevated temperatures (300-900 K), exceeding 1.1. Moreover, the selected APV materials, especially Ca3AsN, Ca3SbN, and Ca3BiN, maintain promising thermoelectric properties also in the medium-temperature range (approximate to 600 K), with ZT values of approximately 0.8, along with unconventional temperature-dependent thermal conductivities. Our work serves as a proof-of-concept example for designing materials for future medium-/high-temperature thermoelectric applications.