I think quite a few people here are making some pretty wild assumptions about ferrets because they know about other animals. Ferrets are not dogs, aren't cats, and aren't hamsters, and knowledge about them doesn't necessarily apply to ferrets. Their needs and tolerances are very different.

My best advice to you would be to consult with other ferret-owners and see what they think about the heat issue... that may be your only sticking point. I have some experience with ferrets, but not biking with one... my initial thought is that if you keep a container of ice in his cage and ample water with him he'll be okay... you'll have to stop and change it every now and then. I second the notion that you should take a short trip and see how he does. It should be obvious if he's not enjoying himself.

EDIT: Also, as was mentioned, taking a siesta in the hottest part of the day and instead riding in the mornings and late into the evenings may help the problem as well.

Cage seems like a non-issue to me. I know it's pretty common practice to cage ferrets while the owners are off at work (8 hours), so I don't think a decent sized cage on a moving bicycle will be bad for the little guy, providing you don't go for too long without a break for outside-time. Ferrets, unlike dogs or cats, are OK to be caged for some time, especially with companionship... it's not bad for the animal. I think the same would go for sleeping - caged in the tent with you would solve litter and shelter problems... just be sure you take lots of breaks and he gets a lot of chances to run about during the day. Again, you know your pet, and you'll know when he isn't happy with things.

I'm very skeptical of animal troubles, but I guess maybe if you're super deep you might have problems.

As far as some states' ridiculous ban on ferrets, this is definitely something to be aware of. Either know ahead of time, or have a way to find out and change plans if you are doing this on-the-fly. They will not let you go through border crossings if it's banned, and getting caught when you aren't supposed to have one will result in a fine and a confiscation of your buddy.

As far as this thread being odd, I'm not sure why. People travel with pets all the time, and ferrets have been domesticated for nearly as long as cats and dogs and served similar purposes (companionship, hunting, etc). Just because it's not a dog doesn't make that weird. Traveling with a pet can be a good experience for both of you... if you can do so in a way that's safe and good for you both, why not? Touring is supposed to be fun, after all.