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.
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.
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.
Phase-change pack hold time is a function of mass, latent heat and insulation, and published figures for small parcels are on the order of one to two days.
The domestic leg is the part you control. Refrigerate it promptly.
edited 18 Sept 2024 by haze_check — added a caveat about sampling