When current flows through a wire continuously, the wire is not heated continuously. Why?
From Joule’s law, we know that when electricity passes through a wire, heat is produced. So, temperature of the wire increases. But as the temperature of the wire rises, the radiation of heat also rises. Radiation of heat tends to decrease the temperature of the wire. A time will come, when rate of production of heat and the rate of radiation from the wire becomes equal. Then the wire attains a steady temperature.