Matt,
Originally I had the stem of the thermometer in the front, extending into the interior space, but when I put in the viewing window I moved the thermometer to the side. With regard to the lamp socket, I simply made a hole in the top of the Styrofoam unit and inserted the socket into that hole from the inside. The fit was a little bit loose so I simply wrapped some duct tape around the socket to get a tighter fit. The socket is raised a bit above the top (exterior) surface of the Styrofoam so all the wires are above that surface. It wasn't the fanciest job but it worked and I have gotten a lot of use out of the proofing box.
Peter