Accepted answer
Because temperature enters the rate constant through an exponential, so equal steps in temperature multiply the rate instead of adding to it. Arrhenius puts the rate proportional to exp(−Ea/RT); the working approximation is a doubling per 10 K, which takes 5, 15, 25 and 35 °C to multipliers of 1, 2, 4 and 8. The steps in temperature are equal and the steps in rate are not, and that is the whole of the observation. At 25 °C the same rule gives about 4 times the refrigerated rate, and another 10 K would roughly double it again. A stereocentre inverts. Identical mass, identical formula; only a chiral method or a peptide map with a chiral digestion sees it at all. Ea differs by route, so the ranking of routes changes with temperature too — which is why accelerated data extrapolates badly and why nobody should read a 40 °C study as a fast version of a 5 °C one.
Answer first: the degradation pathways worth knowing are hydrolysis, deamidation, oxidation, aggregation and adsorption, and each has a different trigger and a different mitigation.
Deamidation converts asparagine or glutamine to the corresponding acid via a succinimide intermediate, adding one dalton. It is base-catalysed, accelerates above neutral pH and is the dominant aqueous pathway for many peptides.
Hydrolysis cleaves the backbone, most readily at aspartate-proline and aspartate-glycine sequences, and is acid-catalysed. In a dry solid it barely proceeds at all.
Deamidation via the succinimide intermediate is well characterised, with sequence-dependent rates highest for asparagine-glycine motifs.
Sequence determines which pathways apply, so general statements are general.
Sequence decides which pathways are even available. Check the residues.