Well, the gourami you won't have to worry about, as they breath air anyway. Cories will do fine in low oxygen water as well as they can breath the air if they need to.
To be honest, I wouldn't worry about air too much in the car. If your power went out in your house or something, that would make me nervous, but in a car you hit enough bumps, and there's enough vibrations that you should have plenty of surface agitation.
As for the heat, why don't you just keep it around 72-75 degrees in your car. The fish will be fine in those temperatures for a few hours, and you won't be boiling either.
Also, don't forget to keep your filter media wet during the ride. And I wouldn't recommend putting the gravel into the same container as your fish, it will make the water very murky and stir up all sorts of trouble. Just keep the gravel moist in a standard 5 gallon bucket.