A red-footed tortoise travels best in a strong, ventilated box with sides high enough that it cannot climb out, a non-slip lining under its feet, and a lid or cover — carried flat and level from enclosure to car to clinic so it never ends up on its back. This is a heavy, deliberate animal rather than a fragile one, and the risks of the trip are mechanical: sliding, tipping, chilling and escaping.
The two accidents you are really preventing
The first is a flip. A tortoise that tips onto its back in a moving box struggles hard to right itself, and a red-footed tortoise left inverted is in genuine trouble, so the container and the way you carry it must keep all four feet pointing down. The second is a slide: on a smooth plastic floor, every brake and corner sends the tortoise thudding into a wall, which can crack a shell edge and badly frighten an animal that cannot brace itself. Footing and level carrying are not comforts for this species — they are the safety system.
Building the travel box
Pick a rigid plastic storage box or stout cardboard box only a little wider and longer than the tortoise, since extra space just means a longer slide. Line the base with a folded towel or a thick layer of newspaper so the feet grip, and add a loosely crumpled towel at one end for the tortoise to push against and hide beside. Punch air holes near the top of the sides if the lid is solid, and use the lid: red-footed tortoises climb better than they look like they should, especially stacked against a corner. Do not add a water bowl, which will soak the lining and chill the animal, and do not travel two tortoises loose together where the heavier can climb over the other.
Warmth and the drive
Red-footed tortoises come from warm, humid country, and a cold car is a real setback for one already unwell enough to visit a vet. Warm the car before loading, set the box on the floor behind a seat where it cannot shift, and wedge it gently with towels so braking does not move it. In cold weather a wrapped warm-water bottle outside the box, against one wall, gives the tortoise a warmer end to sit near without any risk of direct contact burns. Keep the box out of direct sun, which overheats a closed container surprisingly quickly, and drive the direct route rather than combining the trip with errands.
At the clinic with a tortoise this size
Lift the whole box, never the tortoise by its shell edges at arm's length, and keep it level through doors and across the car park. Tell the vet what the tortoise has been eating, whether droppings have changed, and how active it has been, because appetite and behaviour shifts are often the reason for the visit. If the tortoise has been flipped, has a shell injury, or is limp and unresponsive, say so on the phone before you leave so the clinic is ready. Bringing this tortoise's feeding history, housing temperatures and past weights together in its KinsLe Pet Passport gives the vet a reliable baseline instead of guesses reconstructed in the waiting room.