In the manual that comes with my rock climbing rope I bought (black diamond) there's a picture with a death sign when the temperature goes below -62 Celsius. Temperatures outside of planes reach well below this so it's possible the checked bag can hit less than -62 C. So how exactly is it safe to check in rock climbing gear?
Also, I'm afraid of the TSA manhandling my equipment.
As noted in comments by WeatherVane, the baggage area of a commercial flight will never approach anything near -62C. Sitting out on the wing, sure, but consider there is only a thin piece of aluminum between your feet and the baggage are, and your feet don't freeze (and pets and liquids, not to mention fresh flowers, are carried there routinely).
This still leaves the question of understanding just why there is a minimum temperature stated for use of the climbing rope (and potentially other climbing gear). This is because key material properties can change dramatically with temperature.
For many metal alloys (e.g. steel), there is a defined ductile-to-brittle transition temperature. Normally one expects steel to deform slightly (elastically) under stress, and then rebound completely when the stress is removed. If you exceed the maximum tensile (or shear) stress, one expects the material to deform more (plastically), yet stay in one piece until a much higher stress finally pulls it apart.
In contrast, when brittle, an applied stress can result in a small pre-existing crack (and all manufactured items have pre-existing cracks) to rapidly and uncontrollably extend through the material, breaking it in half. The classic example would be Liberty Ships in WW2. But, if there is not an applied stress, there will be no brittle failure.
Your rope is not a metal alloy, but similar principles apply for many polymers - above one temperature they are elastic, below it brittle. Folks living in cold regions know this well, where many normal commercial items (plastic buckets, windshield wipers) will just shatter in sub-zero temperatures. Again, such failure requires a stress to be applied (although sometimes internal stresses are enough). So, yes, the manufacturer of your rope is telling you that your rope will not perform to spec below -62C and may well break upon you taking a fall while the rope is that cold. (You, personally, are unlikely to work to spec at -62C as well.)
A bag of climbing gear should happily take a stint at -62C without major issues. There are no applied stresses (none approaching normal fall forces), so no driving force for brittle failure.
