Ok, first, take a deep breath and calm down. This will all be ok. I assume you already have a plan for moving your little guy. Since he's in shed, you'll just need to make a few adjustments. First, get a cotton pillow case, plain white if you can. Then get a small Rubbermade tub, the 6 or 12 qt size should be fine. Next pick up a hand warmer type heat pack.
Prepare for the move by poking some holes in the tub. When you're ready to roll, soak the pillow case and the wring it out till it's just damp. Place your boy in the pillowcase, and put it in the tub. Open the heat pack and tape it to the underside of the tub's lid. Put the lid on the tub, and secure it with tape or bunge cords. He'll be warm, secure and humid for your trip to the new house. You can even leave him in the tub till you have his enclosure set up and warm.