A method of applying inductive heating to join an integrated circuit chip to an electrical substrate using solder bumps including applying a magnetic field to a magnetic liner in thermal contact with a solder bump on the integrated circuit chip. The magnetic field causes Joule heating in the magnetic liner sufficient to melt the solder bump, which has a lower portion embedded in a first dielectric layer and an upper portion at least partially embedded in a second dielectric layer. The lower portion is in electrical contact with a conductive pad, the first dielectric layer is above the conductive pad and the second dielectric layer is on top of the first dielectric layer. The duration of application of the magnetic field is controlled to achieve a joining temperature that is approximately halfway between the storage and operating temperatures of the integrated circuit chip.