7 hours is really quite a trip and it would be very challenging to do, but I'd say it's not impossible.
Your biggest enemy is going to be the vibrations and bumps in the car. Even holding the bag/bowl/container he's being transported in wouldn't be enough. Try going with a box, preferably a styrofoam box (sometimes called coolers) and put whatever you're transporting him in along with blankets. Just make sure it's super tight and that there's no room for his housing to move.
As for temperature, he probably could live for 7 hours even in less than favorable, room temperature conditions but if you want to be 100% safe, go to an outdoor sporting store (or maybe walmart - I don't go on moral grounds) and purchase a couple of heat packs intended to go in a jacket during colder months. Activate them and stick them in the box snugly around his housing.
Use clean water in the housing and don't drive too erratically to have the best chance of him making it there alive.
Additionally, you could substitute the heat packs with turning the AC off. I can't tolerate high heat for 7 hours, but I may be able to if my betta's life was on the line!
Good luck and safe travels!