Does an insulator reduce heat flux or drop the temperature in this problem?
The insulation will reduce the heat flux AT CONSTANT DELTA T. What will happen is the wire will heat up to give enough more delta T so that the heat leaving balances the heat created. THe temp drop will be across the insulator. Note that heating is I^2R, not IV Note also that the uninsulated wire will have some barrier to losing heat, the ‘film coefficient’ so it will NOT be at the same temp as the air around it.