Does a steady state condition refer to attainment of maximum temperature on a body under uniform heating or (Ts-Ta) is constant at any interval of time?
If there is no temperature control and the furnace is "perfectly" insulated, then certainly the heating coils will melt, because the heat has nowhere else to go and the temperature of the coils will keep rising. Usually, such furnaces are quite well insulated, therefore the temperature controller is very important. I know of a case where, even though the controller was functioning, the terminals of the control thermocouple were inadvertently interchanged and the coils melted down. This is why in the thermocouple sets sold by Omega and other illustrious manufacturers, they have a male-female connection, to avoid interchanging of the + and - of the control thermocouple.