Accepted answer
4 °C is inside or near the refrigerated band. 4 °C is the condition the rule of thumb is anchored to, so it is the baseline rather than a multiplier: everything else in this thread is quoted relative to it. That is the condition most lyophilised peptide is specified at, so the useful question moves to what happens after reconstitution, where the same temperature buys far less. Nothing here is medical advice, and research-use-only material is not approved for human use.
Desiccant matters more than the last few degrees of cold for a lyophilised powder.
Store with the desiccant sachet if one was supplied, inside the secondary container rather than loose in a drawer. Residual moisture is the dominant variable in solid-state stability.
Keep the certificate with the vial, physically or as a photograph filed under the lot code. A vial without a traceable certificate is an anonymous vial regardless of where it came from.
Residual moisture is the dominant determinant of solid-state stability, which is why desiccants accompany lyophilised material.
Keep the desiccant with the vial and the certificate with the lot code.