Go to Wally world, buy a $19 toaster oven, gut it and put the elements in your box. It already has a built-in temperature controller and a relay that can handle a few hundred watts. You can upgrade the relay if you need the full power of your 1500W element from the electric grill.
Don't worry about trying to vary the power to keep the thing from going full power like everyone else is suggesting. Just get a nice big hunk of cast iron and put that between your heating element and the wood chips for smoking. The metal will give you enough thermal mass that you don't need to worry about the element blasting things when it comes on full power. The simple bang-bang temperature control from the toaster oven is quite sufficient to keep the temperature steady on the other side of the cast iron. It'll take a little longer to heat up, but you're going to be doing low and slow cooking all day anyway, aren't you?