Heat transfer through layered wall
I would start with guessing which one represents the "off" state. I would say (D), since the temperature slopes evenly from one air interface to the other, and is fairly constant in the heater layer. Based on this diagram you can also conclude as you did that layer 3 has the lower conductivity. And the slope in layer 2 indicates that it has a finite (not infinite) conductivity higher than that of 1 or 3. 

Based on observations made in (D), you can conclude also that (B) represents the "on" state. As you explain, (C) is not sensible unless heating originates at the interface between layers 1 and 2. (A) also does not make sense, because it suggests that there is a heat sink between 1 and 2 (where is that heat going?).