Grow tomatoes outdoors inside a transparent plastic box

Question

First time I'm going to plant tomatoes. I read up already on how to plant the seeds into pots.

My question is: can I put the pots (containing the planted seeds) inside a big (45 liter), transparent, covered plastic box (something like this), and grow the tomatoes there? (In order to kind of emulate a greenhouse?)

      +---------------------------------------------------+ <---- transparent
      |          /                 \                      |        cover
       \     ~~~|~~~            ~~~|~~~                  /<--- transparent
        \    |     |            |     |                 /    plastic box
         \___|_____|____________|_____|________________/
                ^                  ^
                |__pots with soil and seeds

I suspect the answer is no, because I already tried researching this, and didn't find it anywhere (and I'm sure someone should have already done this, if it was a good idea :)), so the follow-up question is: why is this not possible, what would be the problem if I did so?

In case it is possible, which of the following is the best course of action, and why?

1. plant the seeds indoors, and wait until the plant starts to grow still indoors; when the plants start to grow, put the pots into the plastic box, and put the plastic box outside
2. plant the seeds indoors, and put the pots into the plastic box indoors; when the plants start to grow, put the box outside
3. plant the seeds (indoors or outdoors, I guess it does not matter?), put the pots into the plastic box, and put it outside immediately (this would be my preferred one)

Motivation for this idea: - Keep plants more safe (against wind, cold, insects, etc., also green house is good in general for plants I think?) - Less mess (any spill-over soil ends up in the box -- this is especially important if I have to plant the tomatoes indoors first)

Answer 1

The "greenhouse affect" , the heat will kill them when the sun hits it. The top would need to be opened when exposed to the sun.