I am trying to come up with a method to calculate the maximum current one can push thru a conductor until you reach a predetermined temperature.

What is stumping me is the following: I know the conductor initial temperature, initial resistance, energy that has been put into the conductor (power x time), and the specific heat of the conductor. How can I relate all of this information to determine a final temperature?

Initially I am assuming DC or low frequency AC. Eventually I want to expand the model to include skin effect from higher frequency AC and variable duty cycle waveforms.