The promise enabled by boron arsenide’s (BAs) high thermal conductivity (κ) in power electronics cannot be assessed without taking into account the reduction incurred when doping the material. Using first principles calculations, we determine the κ reduction induced by different group IV impurities in BAs as a function of concentration and charge state. We unveil a general trend, where neutral impurities scatter phonons more strongly than the charged ones. CB and GeAs impurities show by far the weakest phonon scattering and retain BAs κ values of over ~1000 W⋅K−1⋅m−1 even at high densities. Both Si and Ge achieve large hole concentrations while maintaining high κ. Furthermore, going beyond the doping compensation threshold associated to Fermi level pinning triggers observable changes in the thermal conductivity. This informs design considerations on the doping of BAs, and it also suggests a direct way to determine the onset of compensation doping in experimental samples.