Oh, did they say Nashville? If so I apologize for having overlooked that. 
Yep, Nashville AND Portland.
I once had to take our cat to the vet via a long bus journey. He was in a box on my lap, and never stopped repetitively and rhythmically howling the whole way. I don’t really know how long it took (maybe about an hour), but it seemed like forever.
Cat-a-pult.
If you’re going to drive and tranquilize them please for your own sanity try it BEFORE the trip.
I drove from Calgary to Toronto with 2 cats many many years ago and the vet prescibed tranquilizers. One cat dozed the whole way - the other reacted in a very different way. I was seranaded by stoned yowls the entire trip.
Both cats were leash trained and I didn’t crate them - they were in their harnesses with seat belt clips in the back seat with enough slack to reach their litter box and water dish.
What… did no one see The Incredible Journey?
What? No pictures of subject cat! I thought that was a RULE here on the SDMB.
Go with the suggestions of a cold water bottle or similar with ice. Renew ice at evening stops and from drive thru’s. Ask nicely for a cup of ice for your pet. A bigger carrier/cage is good. Possibly add a big stone or ceramic slab you can cool in the hotel room a/c or with ice in the tub for a nice place to lay during the trip. Keep out of direct sunlight. Have cool water available for the cat to drink at all times.
Play cat friendly tunes on the stereo (sorry, don’t have any suggestions). Others can come up with cat-chy titles.
You bury it. Just to be on the safe side.
I have nothing to contribute except I had a friend with two cats that we drove to visit friend’s parents out of state. She put a shallow clean litterbox on the floor in the back and both cats on the back seat (when we heard any scratching in the litter, the plan was to pull into a rest stop, wait till the business was completed, and clean out the litter box and proceed on). The first half hour or so, there was yowling, complaining, and retching (from the cats, that is!) and then they settled down and slept most of the way. … These were unusual cats in that while at the parents house in the country, they were allowed to roam around without a leash. They did not take off into the wild and kept close to us. Return trip, same thing as the trip there…My friend lived in the city. She parked her car, picked up her suitcase, opened the back door, and both cats jumped out and trotted behind her, side by side, down the sidewalk, through the doors, and onto the elevator. Like a pair of well trained doggies. I was just astonished.
So, with that useless anecdote, I wish you good luck and have a tolerable trip!
Yet, one more reason, I currently own no pets.
horsetech’s comments re: sedation have made me very nervous. I have to move my cat from San Diego, CA to Vancouver, Canada later this summer. Driving is out for the reasons discussed in this thread*, but since (a) the cat is very, very, very nervous around humans, and (b) he pees when frightened, I’m not sure how to get him through airport security and into either cabin or freight without giving him a kitty heart attack. I was relying on sedation to help. What is the least evil: hours of sheer terror or hours of sedation-fogged terror? (Cat is 11 and in good health.) Obviously my vet’s advice is going to trump message board opinion, but I’d like to have as much information as I can before I talk to the vet.
*Though I may fly into Seattle and drive him across the border; not sure yet.
Okay, the vid of the guy backpacking with the cat has to be one of the weirder things I’ve ever seen… (not as weird as that “Uri Geller Knows You” site, though.)
If it were just me, I’d never get that AC in the van fixed. (Why would anybody want it in Portland?? I fully expect to wear sweaters almost 365 days a year there. I don’t even want car AC in Nashville and it gets over 100 degrees in the summer all the time. I’m insane that way. 
I would do it for the cat’s sake (he’s named Starbuck, btw)(unless the AC really DOES turn out to be over a thousand dollars to fix)… But the entire thing is just making me so nervous, and it’s getting worse with each new possible complication I hear about. My brother is very cavalier about it all, but he made the trip during cool weather, when it was safe to leave the cats in the van for short amounts of time while he and his gf ate meals, took rest stops, etc. He feels a proprietary interest in the cat and describes himself as Starbuck’s “uncle” (it’s just too complicated to explain.) Well, if so, he should want what’s BEST FOR THE CAT.
I’m going to try to convince him that we should leave Starbuck with his gf’s parents and they can get him over Christmas. Any ideas for good arguments?
Best option is to try it out beforehand.
Talk to your Vet, and sedate the cat sometime when you are just at home, not going anywhere. Or maybe just a short drive around town. Then you can see how the cat reacts to the medication. Do it at a time when you or someone can be there to watch the cat, and during the week when the Vet is available if needed.
I’ve been sedated (as opposed to being totally knocked unconcious) for several surgeries. Before sedation, I was extremely anxious to somewhat terrified. After sedation, everything was peachy keen, and I was enjoying the buzz. In fact, I can easily see how people can get addicted to stuff that takes the worries of the world away. I would imagine that most cats will have a similar experience. A few cats might have an adverse reaction, but I will bet that your cat has a happy experience.
Don’t forget the catnip. Lots of it.
Cat Stevens?
For people who know about cats: What if the cat’s shaved first? That should kind of help them not get overheated, right?
Yes, and should make it considerably less traumatizing.