Elemental substitutions are successfully used for the optimization of thermoelectric properties of a specific material; it requires, however, a deep understanding of its impact. For this purpose, based on the full-Heusler material ${\mathrm{Fe}}_{2}\mathrm{VAl}$, various compounds (${\mathrm{Fe}}_{2\ensuremath{-}x}{\mathrm{Cr}}_{x}\mathrm{VAl}$) were synthesized by substituting Cr for Fe in a wide range from $x$ = 0.005 up to $x$ = 0.4. X-ray diffraction analysis revealed full solubility of Cr for all concentrations. Bulk thermoelectric properties, such as electrical resistivity, Seebeck coefficient, thermal conductivity, and Hall resistivity were measured from 2 K up to 780 K, and all results were discussed in the context of the outcome of density functional calculations. Transport anomalies, resembling Kondo scattering, were observed for all samples below 30 K. Finally, an increased effective number of valence electrons of 7 for Cr was phenomenologically determined, which revealed good agreement with other $p$-type doping studies of ${\mathrm{Fe}}_{2}\mathrm{VAl}$.