A theory for the effect of directed neutral beam injection (NBI) on impurity transport in tokamaks is extended to include temperature gradient effects. The extended theory is compared with experimental data from the Princeton Large Torus, and certain coefficients are adjusted to provide agreement. The adjusted theory is applied to assess the potential of NBI being used to prevent impurities from penetrating to the center of future tokamak plasmas, thereby possibly creating a cold radiating edge. The results indicate the possibility of creating a cold radiating edge in the tokamak fusion test reactor and in future tokamaks represented by the fusion engineering device and STARFIRE.