Accepted answer
Answer first: for a lyophilised solid the cold chain matters far less than people believe, and for a solution it matters far more than they act as though it does.
Arrhenius behaviour means the degradation rate roughly doubles per ten degrees. A week at thirty degrees is therefore a meaningful exposure for a solution and an immaterial one for a dry solid.
Asking a supplier to hold a shipment during a heatwave is reasonable and the better ones agree; the cost is a week and the benefit is a shorter warm exposure for anything in solution.
Solid-state stability of lyophilised peptides at ambient temperature is documented in formulation studies with residual moisture as the dominant variable.
The caveat is that a warm transit is survivable for a solid and materially different for a solution.
Lyophilised tolerates the lane. That is the answer for almost every order.