Re: low temperature correction
the minimum temperatures are associated with GPS/RNAV approaches. As you referred to earlier, there is a preprogrammed set of altitudes in the FMC database for the approach. As you can't (or shouldn't) overwrite these altitudes, there is a minimum temperature that these appraoches can be conducted in. If you were to fly the approach in VNAV (or whatever the vertical mode is in the Airbus world) you'd be low at all the IF/FAF/MDA etc altitudes.
CAT I/II/III approaches do not have this restriction.
Again, it's only the CAT I DA that is corrected.
CAT II/III DH's are based on a radar altimeter.
I think the lowest temperature I did an approach in was -53C. And guess who had to do the walkaround after,......Brrrr!!!