The relevant physics is that a single phase-change pack in a thin-walled box holds below ten degrees for one to two days in a twenty-five-degree ambient, and considerably less at thirty-five.
A single-use temperature data logger costs a few pounds and converts speculation into a record. If the temperature history matters to you, buy one rather than arguing about packaging.
Tracking quality is the more informative signal: continuous scanning at every hop indicates a real logistics chain, and a tracking number that goes dark for a week indicates something else.
Solid-state stability of lyophilised peptides at ambient is well documented in formulation studies, with residual moisture as the dominant variable.
The caveat is that a warm transit is survivable for a solid and not for a solution, and the difference is not marginal.
Ask for a hold during a heatwave. The better suppliers agree without being pushed.