I might suggest making a frame to clamp in the sheet plastic though, by taking strips of wood (heavy enough to keep from flexing), which you can bolt down over the top of the edges of your chamber (use foam tape to get a seal here). That would allow you to use thin Evergreen sheet styrene, without it's simply shriveling up and shrinking when heated, and giving you an airtight seal around the edge of the plastic as well.
Biscuitbuilder1