The use of strong magnetic fields to augment the output energy of inertial confinement fusion experiments at the National Ignition Facility is of high interest. It offers the potential of reducing electron thermal conduction and increasing hot-spot alpha heating with little to no change in hohlraum behavior. In these magnetically assisted ignition experiments, the ultimate goal is to add a B-field in the form of a pulse ranging from 25 to 60 T to a high-performing hohlraum implosion several microseconds before impingement of the laser beams. This requires eliminating metallic components in the target and replacing them with electrically nonconducting materials. However, the strong eddy currents generated by the rapidly increasing high B-field, which were calculated to be as high as 2000 K, can heat the hohlraum. In this paper, we examine the transient effects of this rapid temperature change on the behavior of the target as well as the fuel layer composed typically of deuterium and tritium. Using simulations and calculations for limiting case scenarios, we find that the effect of the heating is not restrictive toward the performance of the target or the quality of the deuterium-tritium ice.