the top is thick enough that it really does keep the heat from radiating through, so if I was somewhere with a lot of sun I'd be leaving the top on the truck and just storing the doors somewhere instead.
When it comes new, it's a really large box. The doors come as complete units, so the box is larger than they are. The top is just folded over a couple of times.
I remember seeing a local National Guard unit that had brand new trucks driving them back to their post. The cardboard boxes on the backs of the trucks were about 6-8" thick, the length of the fenders, and the entire width of the truck