The use of the advanced manufacturing technique of strain annealing for nanocomposite magnetic ribbons enables control of relative permeabilities and spatially dependent permeability profiles. Tuned permeability profiles enable enhanced control of the magnetic flux throughout magnetic cores, including the concentration or dispersion of the magnetic flux over specific regions. Due to the correlation between local core losses and temperature rises with the local magnetic flux, these profiles can be tuned at the component level for improved losses and reduced steady-state temperatures. We present analytical models for a number of assumed permeability profiles. This work shows significant reductions in the peak temperature rise with overall core losses impacted to a lesser extent. Controlled strain annealing profiles can also adjust the location of hotspots within a component for optimal cooling schemes. As a result, magnetic designs can have improved performance for a range of potential operating conditions.