Concretely, the domestic leg after arrival is the part most often left in a warm hallway and least often worried about.
A pack that arrived hard tells you about the last day of transit only, since it will have melted and, if the ambient dropped, partially refrozen.
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.
Single-use temperature loggers are standard practice in supply chains where temperature genuinely matters and are inexpensive at parcel scale.
A cold pack tells you nothing about the eleven days before the last one.
Lyophilised tolerates the lane. That is the answer for almost every order.
edited 5 Sept 2024 by ilaria_bertone — clarified the distinction between purity and content