The underlying point is that degradation is not one process, and which one dominates depends on the condition you are asking about. In solution at refrigerated temperature the rate-limiting pathway is usually deamidation and hydrolysis; at room temperature aggregation overtakes them; frozen, the damage happens during the transitions rather than during the hold.
The temperature dependence is roughly Arrhenius over the range that matters, which in practice means every ten degrees of increase roughly doubles to triples the rate. Ten days at thirty degrees is therefore comparable to something on the order of a month or two at four degrees — bad, but not the catastrophe it feels like when you open a warm parcel.
Degradation pathway by condition
| Pathway | Dominant when | Detected by |
|---|
| Deamidation | Solution, neutral to alkaline pH | RP-HPLC, +1 Da on MS |
| Oxidation | Light, trace metals, peroxides | RP-HPLC, +16 Da on MS |
| Hydrolysis | Solution, extremes of pH | RP-HPLC, fragment masses |
| Aggregation | Agitation, interfaces, high concentration | SEC, visual haze; often invisible on RP-HPLC |
| Freeze-concentration damage | Freeze-thaw of buffered solution | SEC, loss of recovered content |
Adsorption to the container is a real loss at low concentration. For a peptide at 0.1 mg/mL in an untreated glass vial, single-digit percentage losses to the wall are plausible; at 5 mg/mL it is negligible. This is one of several reasons not to reconstitute to a very dilute working solution and store it.
Deamidation kinetics for asparagine in peptides are well characterised and strongly sequence-dependent: the residue following the asparagine dominates the rate, with glycine and serine at the n+1 position accelerating it by an order of magnitude relative to bulkier residues. That is why two peptides in the same buffer at the same temperature can have quite different shelf lives.
I would be careful about generalising across sequences. Stability is sequence-specific, and a rule derived from semaglutide will not transfer cleanly to a tri-agonist with different residues in different local environments.
If the material arrived warm and it was lyophilised, test it and proceed on the result. If it arrived warm and it was in solution, the result is more likely to be interesting than reassuring.