An unsteady flow and heat transfer of an incompressible electrically conducting fluid over a porous rotating infinite disk impulsively set into motion are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed uniform outer radial flow far above the disk on the behavior of the physical flow. The governing Navier-Stokes and Maxwell equations of the hydromagnetic fluid, together with the energy equation, are converted into self-similar forms using suitable similarity transformations. A compact, unconditionally stable, and highly accurate implicit spectral numerical integration algorithm is then employed in order to resolve the transient behavior of the velocity and temperature fields. The time evolution and steady state case of some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are also fully examined for the entire family of magnetic interaction, radial flow, and suction/blowing parameters.