Accepted answer
The relevant physics is latent heat: a phase-change pack holds temperature only while it is changing phase, and once it has melted it is a warm mass.
A single-use temperature logger costs a few pounds, records the whole journey and converts an argument into a record. If the history matters, this is the answer.
Once the parcel arrives, the domestic leg is the controllable part: get it into the refrigerator promptly rather than leaving it in a warm hallway for a day.
Solid-state stability of lyophilised peptides at ambient temperature is documented in formulation studies with residual moisture as the dominant variable.
The caveat is that a warm transit is survivable for a solid and materially different for a solution.
Lyophilised tolerates the lane. That is the answer for almost every order.