Kitchen Large Electric Appliances - Frigidaire Refridgerator moving piece

So I have an old Frigidaire refrigerator (old like 80s) that stopped working on me last month. I for the life of me can't find the model number(maybe X175842-20A).. and I feel slightly dumb for it. Anyways, the issue I was having was that the compressor wasn't kicking on at all, no humming, no fans, only thing that worked was the light bulb inside the door. I started by ripping off the temp control switch inside that was attached to the roof/bottom of freezer because it was giving a slight buzzing sound and I had no idea what it was. I rip it open to find the switch but also some part that moves around in circles in a clear plastic piece. I notice on the bottom of it that it looks like there use to be something that you could twist, like some setting control. It was broken off so I had to use a tool but I turned it around a few times not knowing what it would do. I plugged it back in for the hey of it and what do you know, it turned on and it blowing cold air again. What is this piece? Does anyone know? I'll try posting some pics here in a few minutes.

http://farm4.static.flickr.com/3517/4070941386_38fea52673_b.jpg

Thing on the lower right hand side.