On a normal duplex outlet, cut the tab between the "GOLD colored screw terminals" on the outlet (this isolates one side of the hot from the other on the duplex receptacle), feed your neutral to the white screw, ground to the green case tab. The neutral should be connected all the time, not broken. The ground should be maintained and not broken.
Feed your incoming hot 120 wire (make sure it is off/unplugged) to one of the gold screws (on top) jump off that to your STC power feed and your relay contacts common on the stc..
Connect the STC cooling contact to your other side of your (bottom) receptacle gold screw. (the stc now can make and break power to the other side of the duplex receptacle)
Connect the neutral (white wire) to your STC power feed to power the stc. On your plug, do the same, color to color on the woodhead or other brand plug. Use a adequate cord, ie: #14 for 15 amps, or #12 for 20 amps, #10 for 30 amps.
I'm on linux, not figured out how to use the scanner yet. OR I'd color crayon you a schematic.