Accepted answer
Answer first: for a lyophilised solid, transit temperature matters far less than people assume, and transit duration matters mainly because of what it does to the cold pack rather than to the peptide.
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.
Summer lanes are worse than winter lanes for the pack and no different for the solid, which is why the seasonal anxiety is largely misdirected.
Solid-state stability of lyophilised peptides at ambient is well documented in formulation studies, with residual moisture as the dominant variable.
Lyophilised solids tolerate ambient transit. That is the whole answer for most orders.