When I hooked up mine, I decided not to by pass the temperature controller, and installed an on/off switch for the second element. That way I could turn off the second element, not hook up my DigiQ II and still control the original element from the faceplate.
You will not have to plug them into anything, just connect them together. You will by pass the temperature controller. The two longer neutral wires already connects the neutral post of the original element to the heating source. One long wire runs from the element to the temperature controller, the other long wire already runs from the temperature controller to the neutral post of the power source (plug). So if you disconnect those two wires from the face plate and connect them together with a wire nut that will complete the circuit. If you want the pilot light to work to indicate when their is power going through the circuit, you must connect all three wires together.
In order to connect the wires together you may have to cut off the connectors, strip about 1/4" of insulation off the wires and connect them together with a wire nut.
This is not a picture of the wiring of what you want to do, but it shows what a wire nut is and how it is used to connect wires together:
Wiring Nut
