Answer first: for a lyophilised solid the cold chain matters far less than people believe, and for a solution it matters far more than they act as though it does.
A single phase-change pack in a thin-walled box holds below ten degrees for roughly one to two days at twenty-five degrees ambient, and under a day at thirty-five. On a nine-to-fourteen-day lane the material is at ambient for most of the journey whatever was packed with it.
Solid-state stability of lyophilised peptides at ambient temperature is documented in formulation studies with residual moisture as the dominant variable.
Reconstituted material has a genuine cold-chain requirement and it starts the moment water is added.
The domestic leg is the part you control. Refrigerate it promptly.
edited 25 Jul 2024 by anja_hellstrom — clarified the distinction between purity and content