OK lots of misinformation and speculation has happened over this, so let me jump in here and try to clarify.
The ultra low temperature(ULT) storage requirements of the vaccine have been established based on the activity of the vaccine and knowledge of the particular RNA of the virus. It has taken some time to be certain about the right temperature but it was vital that we got it right. The storage temperature, close on -80 degrees C, is not commonplace for vaccines but we got to the bottom of it in the end.
Laboratory ULT freezers are available in most low temperature physics research facilities at universities as well as in many life sciences departments with molecular biology, biochemistry and related discipline departments. They are not common in many but I wouldn't call them rare either. My own laboratories have four ULT freezers that will go down to about -110 degrees C, if needed. Oddly enough, most are rated down to -86 degrees C, which is close to what's needed for the covid vaccine.
Transportation? Not an issue. Special storage boxes have been produced that are packed with dry ice and are fitted with GPS to transport between countries. Sealed boxes will maintain temperature for 10 days. They can then be transferred either to a ULT freezer or a fridge at 2-8 degrees C for up to 5 days. All the vaccine must be used in that 5 days or discarded. It really wouldn't be wise to vaccinate someone with a vaccine at -78 degrees C!