Without knowing where you live, it's hard to say how much protection is adequate

I wrap my mini-greenhouse on four sides with exterior window insulation film. Double- sided tape on the frame, stretch the film, and attach. I cover the back of the unit with black plastic garbage bags. The theory being that this will absorb the heat of the sunlight during the day and gradually release at night. This has worked for 5 years now. Coldest it got here this winter...about 5 degrees overnight for about two weeks.

North of Detroit 6a. I see negative single digits every year for a night or two.

I was thinking I'd use a couple layers of Vinyl tablecloth covers, melted at parts with a torch and glued with something very strong.

I built mine out of wood. Then I wrapped in many layers of 5 mil. plastic. On the inside, I had 2 inch thick styrofoam. I had a roof on it too. Inside I had a 2 gang outlet with a flood light and a fan. I switched it inside so if the sun was going to be out I wood just turn on the fan. I forgot, I had 2 removable windows. It took me 3 hours to build it and temp. never went below 28 degrees.inside. We do have high winds during the winter. This is staked down and won't blow over. I live in northern Ohio.,,Bill

You'll need a lightbulb inside a structure, lit during the overnight.