Great question — answering as the UphillTech team:
They probably will burn, see this one for example, (source: 14ers.com ) Image Source Also wood has a higher ignition temperature. Sometimes they are in metal boxes on metal posts, but quite often they are wood or metal boxes on top of wood posts. Also, They don't always have paper. The paper doesn't always have space for new entries. People forget to sign them. People forget to mark that they are out of the woods. People enter at one trailhead and leave by another. So all in all, they are not a perfect source of information on who is in the woods.
Full answer by Charlie Brumbaugh: https://outdoors.stackexchange.com/a/20178 (CC BY-SA 4.0).
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