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 2–8 °C the same rule gives about 1 times the refrigerated rate, and another 10 K would roughly double it again. Molecules associate without any covalent change, so the mass is unchanged and a reversed-phase run — which is performed in organic solvent — mostly dissolves the evidence before it can be measured. 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.
This is answerable from the chemistry rather than from anecdote, which is unusual and welcome.
Aggregation is physical: peptides unfold at air-liquid interfaces and associate. Shaking maximises that interface, which is why swirling and shaking produce visibly different outcomes on the same vial.
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.
Metal-catalysed oxidation of methionine is documented across peptide and protein formulations and is why chelators appear in some formulations.
Sequence decides which pathways are even available. Check the residues.