Accepted answer
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.
That is the argument for shipping lyophilised. A dry powder with low residual moisture is chemically stable at ambient for months; the degradation pathways that matter need water.
To be exact about it, anything shipped in solution is a genuinely different risk, because hydrolysis and deamidation proceed in the aqueous phase and are strongly temperature-dependent.
Arrhenius kinetics predict degradation rates rising with temperature, and the rates for a dry lyophilised peptide at ambient are low enough to make short-term excursions immaterial.
Customs and legal considerations are separate from thermal ones and are the more consequential risk in most jurisdictions.
Ask for a hold during a heatwave. The better suppliers agree without being pushed.