For the ride home...secure in a snake bag or pillow case (turn pillowcase inside out so snake doesn't tangle in seam threads...also check the corners and make sure they are SECURE...snakes can find the smallest weakness and tear it open for an escape)...then place the bag in as small a tub/box as you can...put some towels for padding around the empty spaces. A secure lid on a tub will help prevent escape if it should make it out of the bag.

Place the tub/box in a secure spot in the car, away from AC drafts and away from direct sunlight through the windows. On the floor in the back seat is usually a good option. Maybe set some stuff around it to keep it from sliding and bumping around.

Once you get it in the car...don't stop until you get home. Do a drive-thru if you want to eat something. Keep a bathroom break VERY short. Just a few minutes in a hot car can kill her. If you have someone riding with you, then it's a good idea to leave the car running and take turns going to the restroom.

Mostly it's just all common sense stuff.

As for the size of the dome....that depends on the size of your tank, I would think. A big dome will overheat a small tank...a small dome may not help much in a large tank.