The tub is the whole world for the day
Choose the smallest secure tub the animal fits comfortably: a big space lets a reptile slide and brace for hours, while a snug one reads as a hide. Line it with paper towel or substrate it can grip, add a low hide or a scrunched cloth for lizards, and punch the ventilation before the animal goes in, not after. The tub rides inside the cabin, wedged on a seat or in a footwell where it cannot slide, tip or sit in a sun patch through glass, which can overheat a closed box frighteningly fast.
Warmth without hot spots
A reptile cannot warm itself, so the tub's temperature is your job for the whole drive. For most journeys the cabin's own warmth, kept comfortable for you, suits the animal too. In cold weather add a hand-warmer style heat pack taped to the outside of one wall, never loose inside and never under the whole floor, so the animal can move toward or away from the warmth. Put a simple thermometer probe in the tub and glance at it at stops; the dangerous failures are silent ones, like a pack exhausted by hour three of a six-hour drive.
Make it dark, make it quiet
Darkness is the calmest signal you can send. Drape a breathable cloth over the tub so light and passing movement disappear, and keep the tub away from speakers and subwoofers whose vibration reads to a reptile as a world that will not stop shaking. Talk and music at normal levels are fine; what unsettles animals is opening, tilting and peering. If children are travelling, agree the rule before you set off: the tub is not opened, tapped or shown to anyone until the destination, full stop.
Drive like the cargo is asleep
Your driving is part of the care. Accelerate and brake gently, take corners wide and slow, and avoid the rattling shortcuts that save ten minutes and cost the animal an hour of bracing. Plan fuel and food stops where the car can park in shade, and keep stops short; a closed car in sun is a hazard to anything alive left inside it, so if a stop stretches, the tub comes with you under its cloth. Do not feed during the journey: a travelling stomach regurgitates, and food can wait for the far end.
Arrive, then leave it alone
At the destination, carry the tub in still covered, set it somewhere quiet, and only then open it, ideally straight into the waiting enclosure with its temperatures already stable. Offer water first; food can follow once the animal has settled and explored. Expect a day or two of hiding and refused meals after a long drive and count that as normal recovery, not a problem to fix with handling. At the far end, put a follow-up question to KinsLe's Kinny; he answers using the KinsLe Answers library.