Marion, we have run several threads on travelling with instruments and guitars in particular. The feelings are mixed as are the experiences, as you would expect. Baggage handling equipment is NOT instrument friendly. Bert has had a lot of experience with that equipment and as I recall, his advice was to pack the instrument, in this case your fiddle in its tight fitting case--make it so if it isn't-- and then pack it into a shipping box as securely as possible.NOW---Take the box and throw it out of an upstairs window. If you are afraid to do this.....DON'T TAKE IT WITH YOU!!!
Some have had success (me for one) with a guitar in a gigbag hanging in the Carry-On suiter closet, but a lot of planes no longer have them. On the other hand I have also simply thrown the case and all (strapped and locked) onto the baggae cart and I guess I've been lucky. My one case does have a NASTY gouge in it that it got on a plane in bagge though.
I would definitely loosen the strings and be absolutely sure the fit inside the case was good. Wrap it in a small towel if you like too. Allow it to warm up naturally before retuning and you should be OK on that front (cold).
Spaw