An inductive thermal bonding system includes at least one inductive bonding or heating member containing a magnetic E-shaped inductive core and a coil bounding a central member of the E-shaped inductive core. A rigid cover plate allows high and predictable temperature rate-of-change during use and reduced thermal cycling time without risk of detriment. Adaptive solid copper pads on multiplayer bonding regions minimize bonding errors and improve reliability. A cooling system is provided for adaptively cooling both the bond head and the bonded stack. Single and paired inductive heating members may be employed, and may also be alternatively controlled and positioned to aid generation of multiplayer bonding subassemblies distant from an edge of a multiplayer sheet construct.