If you are transporting the bird/animal, remember three important things:
DO NOT hold the creature in your hands; in its eyes, you are a predator and this places added stress on it.
Put the animal in a box and have the car warm. Fill a hot water bottle with hot tap water, wrap it in a towel to protect the bird/animal from direct contact with the hot plastic and carefully wedge it so it will not roll.
Keep the box closed, with air holes, and place directly on the seat or on the floor of the car. Do not hold the box. Make sure that it does not slide around on the seat/floor.