If you put a non flammable material, up next to a flammable material, if the no flammable material reached combustion point, the flammable material will start to burn,
Put up dry wall over the foam, (I think it is highly flammable, or at lest once it does get burning it has a very high spread rate),
then use a spacer of some type, preferable some thing non flammable, (like a short section of steel squre tube cut in 1" lengths and use to fasten the drurock up leave a little space at the base so air can circulate,
if you run a regular wood stove with in 18" of that you can easily get the durock up to 400F easily, (depending on way one runs the wood stove),
if you want to lessen the distance make a steel heat shield and space about 3" out from the wood stove and fasten it to the wood stove, add a fan to move the air between the wood stove and the steel heat shield,
you have infared heat waves off of a wood stove they do not heat the air they heat what it strikes, (like light), and then heats that substance,
so with a heat shield, your putting up a screen to block the rays, and then using air to remove the collected heat, yes you have convection heat as well (heating the air), but that is the difference of the feel of heat from a wood stove and a gas air heater,
IF I needed to move a wood stove up close to a wall for some reason, I would most likely make a steel heat shield about the wood stove, like stated above, about 3" out from the stove, then a second one between that shield stove and the wall, and finally some thing like durock with 1" spacing up next to any flammable surfaces, (three heat shields),
but even with all the shielding I suggested, I would still not have the wood stove any closer than 12" to any thing flamable on the sides, or above.
wood stoves can do glow red, (so from the chart below) If you can see that it is red in day light, you close to 2000F degrees on the surface of the stove, and this is a extended heat, it really does not take that long to heat up other surfaces near buy,
Red heat is what temperature
Answer:
C F Color
400 752 Red heat, visible in the dark
474 885 Red heat, visible in the twilight
525 975 Red heat, visible in the daylight
581 1077 Red heat, visible in the sunlight
700 1292 Dark red
800 1472 Dull cherry-red
900 1652 Cherry-red
1000 1832 Bright cherry-red
1100 2012 Orange-red
C= Centigrade
F= Farenheit
IF you have foam exposed cover it all with drywall, or some type of wall covering, (most all have warnings on it to cove it do to the flammability of the substance, (all walls, not just the stove area),
and even if you do choose to use this idea,
YOU ARE the person RESPONSIBLE 
