<p>The electronic, elastic, and thermal transport properties of the derivatives Fe_16−xCo_xNbSb, FeCo_xNi_xNb_8−2xSb, FeCo_xNi_xNb_8−xSb_8−x, and Fe_8−2xCo_xNi_xNbSb (x = 1)&#xa0;of the half-Heusler alloy FeNbSb doped with Co and Ni elements were comprehensively characterized by density functional theory. The stabilities of the half-Heusler alloy FeNbSb and its derivatives were evaluated through phonon dispersion spectra, formation energies, and the Born criteria, and their elastic constants satisfy the mechanical stability conditions. Through the analysis of the band structure, it was found that the half-Heusler alloys FeNbSb and Fe_16−xCo_xNbSb are semiconductors with band gaps of 0.895&#xa0;eV and 0.547&#xa0;eV, respectively. To further understand the electronic structure, assist in analyzing the composition of chemical bonds, and comprehend how different atomic orbitals participate in bonding, thereby gaining an in-depth understanding of the chemical and physical properties of the materials as well as the electron transfer situation, a systematic study and discussion on the atomic orbital projections of the electronic band structure were carried out. The calculated elastic properties indicate that both the half-Heusler alloy FeNbSb and its derivatives possess good ductility and hardness. Utilizing the elastic characteristics and through the Slack model, the lattice thermal conductivity of FeNbSb at 300&#xa0;K was calculated to be 28.74 W/mK; this value is close to the experimental value. Based on this, it was deduced that the lattice thermal conductivities of its derivatives Fe_16−xCo_xNbSb, FeCo_xNi_xNb_8−2xSb, FeCo_xNi_xNb_8−xSb_8−x, and Fe_8−2xCo_xNi_xNbSb at room temperature are 21.57&#xa0;W/mK, 29.25 W/mK, 18.76 W/mK, and 27.2 W/mK, respectively, which may provide an important theoretical basis for experiments and provokes further study.</p>