If it doesn't have a dial on the generator, look below the door and see if there is a slider switch that controls the temperature. It should be labeled "Temperature Controller". If that slider is there then it is The Black Bradley Smoker BTIS1.
They discontinued that model about 3 - 4 years ago. I've had that model for over 12 years, and it is still easy to get parts for it. There are still a few sellers out there that are selling them new for $403 on Amazon.com; which is way overpriced.