Dynamic thermal modelling

I want to build a model allowing to compute the temperature in various places and in time of a notched silver strip surrounded by sand and heated by an AC current. RMS current value, notches depth , shape and pitch being adjustable and not identical all along the strip. The main focus will be on the quick temperature variation due to the 50hz current which follows a sinewave, and the heat transfer between the notches, the plain width parts of the strip, and of course the surrounding sand. Although melting time can take hundreds of seconds, the model must be able to calculate temperature evolution in milliseconds when melting temperature has been reached in one point (time at which current is interrupted during some milliseconds and may be simulated to restart at higher value). Model to be built, calibrated by comparison with existing experimental values , and then should be able to simulate different notch patterns and currents. Price can be in 2 steps : for model building and calibration , then per simulation of silver strip notches pattern.