A warm arrival is a reason to test, not automatically a reason to discard. Peptide degradation is kinetic — rate multiplied by time — and a few days at thirty degrees in the solid state is a small integral compared to weeks in solution.
Practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.
The licensed semaglutide and tirzepatide presentations carry in-use periods of several weeks at room temperature in their labelling, which is the closest thing to real stability data in this space — and it applies to a buffered, surfactant-containing, preservative-containing formulation, not to a reconstituted research vial.
I would be careful about generalising across sequences. Stability is sequence-specific, and a rule derived from semaglutide will not transfer cleanly to a tri-agonist with different residues in different local environments.
The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.