Grats on getting an offer
Four hours is a little while but your axies should be okay as long as they are kept cool during transport, after all, people manage to ship them overnight and things like that.
Go into your local fish store and ask for their biggest fish bags, they should only cost you like 20 cents each, the girl in my LFS showed me how to correctly tie the bag up and everything. Don't use too much water and hopefully you should have enough oxygen in there to last the trip.
If you're really worried, do a Google search for "breather bags" and have a read up on them, the plastic they are made of allows the transfer of oxygen and carbon dioxide so you can fill the whole bag up and your axolotls will survive just fine (this saves the stress of the water sloshing around and things like that).
Though, this might be a bit much for a four hour trip.
As for the temperature, get a styrofoam box and use a frozen plastic ice block or bottle to keep the temps low. The styrofoam should work effectively to keep everything inside it cool enough. Make sure you somehow secure the bag your axie is in in the box so it doesn't move around, otherwise you might find yourself with some stressed out lotls when you arrive!
Good luck