there are several threads loaded with good info on this kind of project already, but I just got around to loading up my images of my recent fermentation chamber build, so here they are. Unfortunately I was in too much of a hurry to take pictures along the way, so I just have the finished product.
Inside dimensions are 45"W x 30"H x 24"D. I used 2x4 and 2x2 framework to house the 1.5" blueboard Styrofoam so that it is flush to the frame. I skinned the frame on the outside with 1/4" luan and some leftover composite (masonite) paneling. I skinned the inside with flexible rubber shower wall liner material from Lowes, and sealed it all up with caulk so it can be easily cleaned etc.
I work with this kind of styrofoam a lot so I am very familiar with how it behaves. to cut it you can use just about anything you want, a razor knife with a sharp blade works fine. I prefer the snap blade knives because the blades are easy to replace and they can be extended so they are longer than the material is thick.
I also frequently use a band saw to cut this material, and have run it through the table saw with no problems as well. I have also used hot (electrified) wire cutters, and angle grinders to shape this material (not that you need them for building a box from it)
The best adhesive for Styrofoam board is 3M Super 77 spray adhesive applied evenly to both surfaces allowed to dry until they are tacky, then align the pieces and press firmly (be sure you get it right because it can be hard to undo). This is a very strong bond, but I'm not sure I would rely on it to hold edges together without some other kind of structure. when adhering to another flat, porous, surface this bond will be very strong. layers of the foam can be laminated together this way too.
For cooling I originally tried an small thermoelectric fridge...which sucked, so I went to Best Buy to look at better refrigerators and I happened to notice a Frigidaire 5000 btu air conditioner (model #FAX054P7a) for about the same price. It is very compact and has a built in thermostat that actually regulates temperature based on degrees, as opposed to a blind "cooler/warmer" knob. This eliminates the need for a separate Johnson or Ranco controller for keeping things at ale temperatures.The downside is that the lowest the thermostat goes is 60 deg F, so its no good for lagering unless the thermostat can be overridden.
Since I am using this fermentation chamber primarily for ales (combating the Florida heat) this suited me fine.
So far it works great, and it sure beats having my carboys in buckets with ice packs in the kitchen....SWMBO agrees