Thermomechanical processing combining plastic deformation and heat treatment is a favorable way to enhance the performance and lifetime of bimetallic laminates, especially those consisting of metals, which tend to form intermetallic layers on the interfaces when produced using methods involving increased temperatures. The presented work focuses on optimizing the conditions of thermomechanical treatment for an Al + Cu bimetallic laminate of innovative design involving a shear-strain-based deformation procedure (rotary swaging) and post-process heat treatment in order to acquire microstructures providing advantageous characteristics during the transfer of direct and alternate electric currents. The specific electric resistivity, as well as microhardness, was particularly affected by the structural features, e.g., grain size, the types of grain boundaries, and grain orientations, which were closely related to the applied thermomechanical procedure. The microhardness increased considerably after swaging (up to 116 HV02 for the Cu components), but it decreased after the subsequent heat treatment at 350 °C. Nevertheless, the heat-treated laminates still featured increased mechanical properties. The measured electric characteristics for DC transfer were the most favorable for the heat-treated 15 mm bimetallic laminate featuring the lowest measured specific electric resistivity of 22.70 × 10−9 Ωm, while the 10 mm bimetallic laminates exhibited advantageous behavior during AC transfer due to a very low power loss coefficient of 1.001.