This is how I use a heat gun to make styrofoam look like brick or stone.
Step 1: Build a Suitable Frame
You will need a framework to attache the styrofoam to. Construct this however you like from wood, metal or whatever. Heck, maybe you have an existing wall you want to make look like brick. If that is the case, then you are one step ahead to start.
Step 2: Attach the Foam
Attach the styrofoam to your frame. In my case I used foam board adhesive on the wood structure I had built. Use small blocks of wood with a screw going through it to secure it while the adhesive dries.
Step 3: Mark & Layout Your Grout Lines
I went for a standard staggered brick pattern. I laid out the grout lines using a straight edge and permanent marker. On the right side you can see the completed brick.
Step 4: Carve Grout Lines
Using a sharp utility knife, a woodworking router or a hot knife, carve shallow "V" or "U" cuts marking out the grout lines 3-dimensionally. You can also do this for large cracks in the brick. I did all of this freehand to give it a more organic look.
Step 5: Heat Gun for Texture
Using a heat gun, start by moving over all the grout lines to give them a cement texture. The grout lines will widen during this process and become more life like. Then move on to the field of the brick. Set the heat gun to a medium texture to start and do some test areas. Keeping the heat gun in one spot for longer or heating closer to the foam will add a deeper rougher texture. I have done this whole process many many times and fumes are minimal but to error on the side of caution I recommend wearing a respirator to keep your lungs safe. Pictured as well are some close up shots to show how real the texturing can look. Use drywall joint compound to hide any seams in the foam.
At this point I also add some window surrounds glued on with the same foam board adhesive to give it more visual interest and to break up some of the larger areas.
Step 6: 6 - Paint the Surface
I like to use a paint sprayer to finish with. It does a much better job in preserving the texture you worked to get. If you don't have a sprayer available, you can use a high nap paint roller as well. Keep in mind if you roll it, you will loose some of the texture to paint filling the surface. Do a test section to make sure you get the desired look.
Step 7: 7 - Add Other Elements
To really sell the real look, add ivy or vines. You can also do some shading with the paint to give it depth and a more aged appearance. And Ta Da, you are done!