Could use sheet rock AKA gymson (sp) board instead of the plywood - THAT stuff is highly fire resistant and I'm pretty sure it handles higher temps than wood.
I find it difficult to believe plywood would ignite at such a low temp though, since PAPER doesn't ignite 'till well over 200C for most grades of paper.
instantly? no, but over time.......say, 2-3 months? possible.........+ a spark? shorted circuits? electrical wirings? you get the idea