Almost all modern aircraft are pressurised including the cargo compartment and are kept at a reasonable temperature above 0C. The cabin altitude is about 8500’ maximum at cruise level, with a rate of climb normally about 500 feet per minute and descent around 300 feet per minute to be kind to passengers’ ears (especially as you don’t get the boiled sweets handed out by the cabin crew any more).
I don’t know how sealed “sealed cabs” are, but if you can put one in the back of a car and take it over the Alps or the Rockies without it exploding, then it shouldn’t explode in an aircraft either. I won’t guarantee that though, as I say, I don’t know how well sealed the cab is. I guess that the high-end cabs like Barefaced are delivered to foreign climes by airfreight, although again, I don’t know.
A flight case would be essential to prevent the curse of the baggage handlers IMO.