The OP asked about shipping with your own supplies through Ship Your Reptiles, not a general question about insulation and temperatures. I personally prefer 3/4'' for normal shipping but it doesn't really matter here. Ship Your Reptiles requires a minimum 3/4'' insulation to use their shipping service.
From their website:
Insulation lining must be at least ¾ inch thick. The insulating lining must cover all four sides of the inside of the cardboard box, as well as the top and bottom.
http://www.shipyourreptiles.com/en/g...s/#question-20