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 minus 80 °C the same rule gives no useful multiplier at all, because below freezing the reaction is no longer happening in bulk solution. Backbone amide bonds cleave, so every product is shorter than the parent and the mass ladder they leave behind is the evidence that it happened. 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.
Asparagine and glutamine are the deamidation risk, and methionine is the oxidation risk.
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.
A mass spectrum resolves most of this: minus eighteen is dehydration or succinimide, plus one is deamidation, plus sixteen is oxidation, and an unchanged mass with a shifted retention time is an isomer.
Deamidation via the succinimide intermediate is well characterised, with sequence-dependent rates highest for asparagine-glycine motifs.
The caveat is that none of these pathways can be seen by looking at a vial, and a clear solution can be substantially degraded.
Cold, dry, dark, still. Those four words cover most of the mitigation.