A smoker is an environment that the user fills with smoke and regulates the heat inside.
Your current smoker is allowing so much heat to escape that you are unable to provide enough hear to keep up.
Looking at the Just-rite web site it appears that these cabinets are designed to keep flammable liquids from igniting in the event of a building fire.
I am not sure if this is a good candidate to convert to a smoker for several reasons:
You might be able to sell it to someone to use for it's intended purpose and collect enough from the sale to pay for all of the pieces to build yourself a really nice smoker.
The insulation in the cabinet might not be a good choice. I am not sure of what they are using for insulation the web site only says 2 inches of high density insulation. It looks like the spec they are designed to comply with is:
Storage cabinets shall be designed and constructed to limit the internal temperature to not more than 325ºF. when subjected to a 10-minute fire test using the standard time-temperature curve as set forth in Standard Methods of Fire Tests of Building Construction and Materials, NFPA 251-1969.
Here they want the cabinet to prevent the solvents inside from going over 325ºF for 10 minutes. A record safe has a similar spec, but that is that it must not allow the content of the safe to be over 350ºF when baked in a fire at 1450ºF for one hour. With a fire safe, the insulation is a cement based slurry that has in it's matrix material that retains water until heated, then it releases water vapor into the safe. It works really well but it is a one time deal, once the water is gone it doesn't insulate too well.
If you look at insulation they use in ovens, what they have is fiber glass or ceramic fiber that slows down the rate that heat can pass through so that the oven can be maintained at temp. This type of insulation is what you want in a smoker as you want to be able to cycle the temp up and down over many cycles without loosing efficiency of the insulation.
Newer refrigerators and freezers use a foam to do the same thing but there the concept is to slow down the heat from coming into the box. Foam is not really good for a smoker as the foam does not like getting hot, so it will melt and burn releasing all sorts of nasty tasting and potentially toxic stuff into your food. If you have ever tossed a Styrofoam cooler into a camp fire and got a whiff of the smoke you might have an idea here.
Your fire cabinet is also coated on the inside with paint. This will have to be burned off before using the cabinet for food smoking. This will probably cook off the insulation.
Two commonly available household appliances are really slick things to convert to a smoker. A regular household oven. It already has a burner, and the right kind of insulation. The best kind is one that is self cleaning because it has lots of insulation as it has to get to about 900ºF long enough to burn off the crud inside with out catching the kitchen on fire. The drawback to converting an oven is that the size of the oven might be a bit inconvenient for hanging a bunch of hams or sausages.
Another candidate is an old fridge from the 40's or 50's. These have nice enameled steel interiors and the tall box is convenient for hanging stuff you might be smoking. I also think most of them have fiberglass insulation although some have a cardboard type paper insulation that needs to be removed. Often the panel on the inside of the door needs to be replaced, but that is easy. You then need to remove the refrigeration works and replace the door gasket with some stove rope. Now all you have to do is to install a burner and some form of control (Easy with electric and a PID ) and then you need to have some provision for smoke and vents. With this set-up you could control your temps in arctic conditions and in the middle of the Mojave with ease.