Put another way, 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.
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.
The limitation is that you cannot detect slow aggregation by eye until it is well advanced, so a clear vial is weak evidence of an intact one.
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.
edited 28 Jul 2026 by fibre_or_fragment — corrected a unit error in the worked example