Just to add my experience to the discussion about thermoforming on the kitchen table.
Thermoforming is normally a quite simple industrial process but has some points which need attention. Most thermoplastic materials can be deep-drawn over a mould or into a negative mould. But some plastics have a very narrow temperature range within the sheet can be deformed and stretched. A typical example is polycarbonate (PC), an other wise excellent material but hard to form if the temperature is not "just right".
One of the easiest to work plastics is polystyrene (PS) with a large temperature band and easy to find in thin thicknesses like plates, glasses and the like. It is also easy to evaluate as it will melt touching it with thinner like acetone. The same applies to a parent plastic, ABS (Acronitrile – Butadiene – Styrene), more resilient and flexible thanks to the butadiene (sort of rubber). But unfortunately not available transparent.
Second point is SPEED. The thin sheets we use have very little thermal inertia and cool down immediately either during the transport from the heating station or at the first contact with the mould. As for the transport you can only be aware to heat the sheet near to the forming mould.
You can do a lot during the forming process to speed up the forming. Try to have a good seal between the plastic sheet and the perforated box top. I use foam strips as used as windows seals. Try to keep the void volume as small as possible. As most of us use the vacuum cleaner which is not a champion of air removal try at least to have little air to extract. If you look at my box bellow you will notice it is quite voluminous, the reason is that the hole for the cleaner hose has a certain diameter. To remove the void volume inside the box I placed a foam block to fill about 90% of the space. Don't be afraid about reducing the space, the air will always find his way out
Prepare more than one frame to fix the plastic on it. I have one which covers the space of a normal A4 sheet of paper and a second one for an A5 sheet. If I use the small one I cover the outside holes with tape and put foam tape to form a gasket around the frame. To simplify and speed up the preparing I spill the plastic to the plywood frames rather than use clamps. So the plastic with his perfect surface acts well to seal the volume to be extracted. You may also continuing to heat the sheet with a hot air gun during the actual forming, sometimes this allow to draw the corners down.
Urs