These vaccines needs to be stored at particularly cold temperatures; some say -20oC and others -70oC, although it may depend on how soon the vaccine is expected to be used. This is far from insurmountable, but nor is it totally straightforward, as very few refrigerated trucks are designed for that sort of coldness and there are huge quantities of vaccine to deliver.Refrigerated trucks are nothing new, especially when talking about medical supplies - a lot of injected mediations have to be kept cold to stay good. Depending on how cold we're talking either a refrigerated truck or shipping it in a dewar - neither is super difficult.
I would also guess they are not using a dewar: that's going to be stupidly expensive and impractical. Conventionally most chemicals companies pack these sorts of unstable molecules for transit (e.g. for biological research) in a polystyrene box filled with dry ice. I'm guessing they are probably using something intermediate between polystyrene and a dewar filled with dry ice.