Does an insulator reduce heat flux or drop the temperature in this problem?

Imagine an electric wire that is generating energy according to the relation VI where v and i are the voltage and current in the wire. Now we place a thermal insulator around this wire whose coefficient of conductivity is k. It seems like the insulator would initiate a temperature drop (inside and outside) but not inhibit the heat flux because of the steady nature of the problem (energy in= energy out). Is this true or not? if it reduced the heat flux, some energy would be missing from the equation. correct me if im wrong thanks