Accepted answer
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.
Light matters for specific residues rather than in general. Tryptophan and to a lesser extent tyrosine and methionine are photo-labile; a sequence without them is largely indifferent to ambient light over the timescales in question. Amber glass is cheap insurance rather than a requirement.
The part that matters: aggregation is the failure mode that reverse-phase HPLC is worst at detecting, because a large soluble aggregate may not elute at all and an insoluble one is filtered out during sample preparation. If your purity result comes back normal but the vial looks hazy, believe the vial. Size-exclusion chromatography is the method that sees this.
Where community-submitted samples with known thermal excursions have been tested at Janoshik or Medutest, the recurring finding is that lyophilised material tolerates warm transit far better than intuition suggests, while reconstituted material shipped warm does not. The asymmetry is consistent enough to plan around.
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 6 Sept 2024 by vialroom — reworded for clarity after a comment