You've got yourself one of the top-of-the-line electric skillets. What made Farberware so unique was not only their elegant styling (much prettier than the Sunbeam or Presto, which were fine skillets, but they didn't have that shine), but the fact they were made of stainless steel. Many of the others on the market were heavy gauge aluminum. These were designed so that you could cook "tableside" or use them on a buffet as a warmer because they were so nice looking.
I have a couple. They cook beautifully and provide very even heating across the bottom of the pan. The same model that you purchased was also available with an "extra-high" lid, so you could prepare a chicken or standing roast.
As far as the thermostat control, yes they do get warm. I think it is, in part, because of the proximity to the heating element. Anything that is right up against the bottom side of that skillet is going to get hot. In my experience, it hasn't had any impact on the performance of the thermostat or has it harmed it in any way.
It is also a nice feature that you can completely immerse the skillet in water to clean (not the thermostat control, though, just wipe with a cloth). It cleans up beautifully. It perfect for browning things (chicken, pork chops) and does a wonderful job with swiss steak, chicken ala king, sloppy joes, and much more. The electric skillet is one small appliance that I wouldn't want to live without.
Enjoy your new find and I hope you make lots of wonderful dishes in your gleaming Farberware skillet!