Why in the world would anyone select MDF for a project like this? MDF is flat and smooth, so it's good for laminating. It's also heavy and that's why it is used for kitchen counter tops. It has no grain across the panel, but it does have grain INTO the edge, so it splits easily when edge fastened. It is also subject to degradation when it gets wet. Using MDF gives you the worst of both worlds; i.e. your annealing machine ends up being heavy and the perceived advantages to using a material thick enough to edge fasten with ordinary fasteners is actually a time bomb waiting to go off.
I would recommend buying a half sheet of high quality 5mm plywood at your local DIY outlet. It's smooth, strong, and ready to finish; easy to cut too and you can true up the edges with a low angle block plane. Yes, it's too thin to edge fasten, but if you take a few minutes to glue in some 1/2" square stock on the edges using ordinary yellow glue, you can make a lightweight enclosure which will be very strong without fasteners except perhaps for a few small brads to hold the parts in alignment. Light, high quality material like this is very easy to work with hand tools, so you don't need access to a table saw. And it will look good too.