Yes, and with the high auto-ignition point of wood combined with a lack of oxygen supply in the enclosure, even if the surfaces somehow reached 800F, a fire could not be sustained. The surface would likely char and that would be the end of it. I used the cement board to provide an extra safety margin with my large and hot 120V bulbs, but it was probably overkill.
I am wondering, however, if your 12V automotive bulbs will be warm enough, but that depends on your lowest ambient temps. Does it get down to 0F where your are?
Our average winter temps sit around 36F. The lowest can reach down to 22F by Feb. and the higher can hit 56F still before early Jan. The winters here usually sees very little snow. If it happens, the snow is gone before the evening sun setting.