If you are keeping a dog on the roof of the car, especially for such a prolonged period, you need to ensure he is protected from the elements, but has appropriate ventilation and periodic stops. Keeping a dog on the roof of your car is a safety concern, and having a lack of direct contact on the dog's condition is a health concern. For an inferred sustained, 12-hour, non-stop period, it certainly does not appear to be a humane way to transport a dog.
Assuming the dog is traveling with you, the safest and proper way to transport a dog is in a controlled environment: inside your vehicle, with the appropriate air conditioning or heating enabled.
The reactions of dogs traveling vary, but if you plan to drive for a long while with your dog, you should familiarize your dog's in-car behavior with a number of short drives. As it stands, the dog should lay down on a seat, possibly with a blanket to grip, or a carpeted area. If there is no carpeting and it is a smooth metal floor, such as the inside of a van, consider a rubber-bottomed floor mat so he can stay stable. If the dog is larger and sits with a seat belt, do so. If you need to keep Fido in a dog carrier in the car, do so. If you have a dog crate and want him in it, make sure it is secure so it doesn't slip or move around in the car.
Equipment / Provisions
Bring a heavy blanket for the dog to rest on. This should give him a good grip for balance. Bring along some kibble and water and a drinking bowl / container for the water. Bring a heavy leash so your dog does not leave your grip when you walk him. Bring some disposable plastic bags to pick up waste, and a roll of paper towels and hand sanitizer in case you get soiled. Bring some cloth towels as well.
Bring a copy any of your dog's identification documents including microchip information if you have it, and vaccination documentation as well as your dog's veterinarian contact information.
Provide drink at rest stops or if you provide it in-car, make sure it won't spill and keep the water level low. Provide kibble at your discretion. Consider how your dog normally schedules his relieving in relation to consuming.
Identify rest stops / parks on the trip map. Plan some stops at grassy areas / rest stops and try to base your schedule on how you generally schedule your dog's outside periods. Do not let your dog go off on his own in unfamiliar areas.
Check the answers to the following related questions for additional helpful advice: