I was wondering if there was any type of Vinyl or Plastic sheeting that you can adhere together by Melting it? to make a box or something?
For diy you can use chloroform, it is used to stick plastic together by dissolving the contacted areas. Most sign makers and art/craft makers are using it. Hot mouldings are usually used by the manufacturing industry.
There is vinyl tape that comes in different colors that would work for that purpose. (not duct tape) The problem with melting vinyl is that it creates a poly vinyl chloride gas that's extremely toxic.
I believe you would have to do a cold-weld. Applying heat to vinyl or plastic is dangerous because of the fumes/fire. For a box, think about plexiglass. Plexiglass is very durable but scratches easily. The thickness of the plexiglass is; 1/8, 3/16 and 1/4 inches. The 1/4 thk. requires a fine-tooth blade to cut. The other 2 can be cut with a box-knife by passing the blade over about 6 times and then using a support edge can be snapped off. You can assemble using corner angles and small self-threading screws but pre-drill first.
