In a School bus i renovated (156sq feet) i had a good sized wood stove due to the lack of insulation and multitude of windows, The walls below the windows had 3inch of pink rigid foam with T&G pine over it. Behind the wood stove i used 1/8inch steel. to mount it i put some d nuts in the wall, drilled holes in the steel plate then had 2 inch piece of steel tubing between the steel and the wall. Then i used hex bolts to bolt the steel to the wall. The stove sat 2 inches in front of this steel. The steel went up higher than the stove covering some of the window. I had the stove cranked many times (top temp in the winter was 40degrees C at head height) and the air and the back of the heat shield was never hot.
I am currently renovated a 12x15 tiny home that was 6x15. whoever put the wood stove in there before just used tin roofing screwed right to the studs over the vapor barrier. The vapor barrier was melted/gone/stuck to the tin roofing when i removed it.
from my experience the heat shield behind the stove should always have a space behind it for air flow.
