Accepted answer
Whatever the refrigerated figure is, divide it by about 11. 40 °C is 35 kelvin above the 5 °C middle of a 2–8 °C refrigerator. The ten-degree rule of thumb — degradation rate roughly doubling per 10 K — makes that about 11 times the refrigerated rate, which is an order-of-magnitude statement and not a shelf life. So a preparation with a twenty-eight day refrigerated figure has roughly 2 days at 40 °C on the same assumption — an order-of-magnitude answer, not a shelf life, and it says nothing about sterility, which has its own clock. "Within specification" also needs a specification: purity, content, or both, and at what limit. Without that the question has no numerical answer at all.
Aggregation is a physical process and is the one most often caused by handling rather than by time.
Oxidation targets methionine, cysteine and tryptophan, adding sixteen daltons per oxygen. It is catalysed by trace metals and promoted by dissolved oxygen and by light.
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.
Metal-catalysed oxidation of methionine is documented across peptide and protein formulations and is why chelators appear in some formulations.
Nothing here is medical advice, and research-use compounds are not approved for human use.
Swirl, never shake. Aggregation is a handling problem more than a time problem.