Also, if you can get a large STYROFOAM storage container, that would have extra insulating power. Just put the lid on, turn it upside down, and cut a door in it.

That way, it has a floor. You may want to glue the lid on to make it watertight.

Would the built in water and food dishes be removeable? You might need that sometimes.

Not sure if you would need a heat lamp...if you had old bits of down-filled fabric and some straw, that might be all they need with styrofoam.

Have a look at some doghouses, and you might get some good ideas!

This is great - keep us posted!