A model describing the transient thermal behavior of an insulated electric wire is presented. The transient temperatures in both conductor and insulator result from the energy generated in the conductor by means of an alternating electric current that fluctuates in any specified manner. The mathematical model is solved analytically using Green＇s function method. The effect of many parameters on the transient thermal behavior of the insulated wire is described The cooling rate from the wire is evaluated at different values of the insulation thickness, and then the effect of different parameters on the critical thickness of insulation is investigated.