Hi Oder4u;
Welcome to the forum.
I have never done it, or have I read any member doing this. There have been members that have converted refrigerators to smokers, but the interior walls were metal or they replaced the plastic walls with metal ones.
Are you just going to place the Bradley in the refrigerator and close the door? If so you are going to have a problem with the smoke circulating, and possibly not getting enough oxygen for the bisquettes to smolder. Though the exterior of the Bradley doesn't get hot, being in a tight enclosed space may cause heat to build up. So you would need some type of intake and exhaust vent system. Or you may want to leave the refrigerator open or at least partially opened.
Also, not knowing the interior size of the refigerator, once the Bradley is inside you may not be able the open the Bradley door far enough to move racks of food in and out of the smoker.
If you search the forum, you will see that many have built, or purchased cabinets to house their smoker. This may give you ideas on how to convert the refrigerato inot a cabinet, or you may want to build your own cabinet. Wind is the main factor in keeping cabinet temperatures down. So any structure that helps block the wind from flowing through the side and top vents will greatly improve the temperature performance.