Only the front 16" of the barrel gets warm on the underside where the firebox is located but not burning hot. The back half of the evaporator has insulation and brick so the heat doesn't escape.
Printable View
As long as the evaporator is insulated well enough, it shouldn't be a concern. I'm more concerned with random embers getting out the door when I add wood.
Also, the hotter area is the single wall stove pipe, so any area that is close should be well insulated from the heat.
Ok My 2x6 has no floor so I have galvanized roof metal plus a layer of fire brick on top and it gets pretty warm. maybe its not insulated enough?
My 2x3 sits on a wooden floor of 2x10s. The firebox has a bottom and I have that bottom covered with firebrick. No heat at the floor. In front of the arch I have a piece of flagstone about 24x 24. That takes care of any coals that might at times fall out of the arch. Your draft should keep any embers going up the stack.