Accepted answer
25 °C is above the refrigerated band, and how far above is the whole answer. 25 °C is 20 kelvin above the 5 °C middle of a 2–8 °C refrigerator. The ten-degree rule of thumb — degradation rate roughly doubling per 10 K — makes that about 4 times the refrigerated rate, which is an order-of-magnitude statement and not a shelf life. Lyophilised material tolerates this far better than solution does, which is why it is shipped that way, but "tolerates" is a statement about weeks and the vial is being asked about months. Log the excursion rather than guess at it. Nothing here is medical advice, and research-use-only material is not approved for human use.
Answer first: dry, cold, dark and still, with the lot code where you can still read it in a year.
Keep vials in their original carton or in an opaque box. Light exposure matters for tryptophan-containing sequences and for anything with a chromophore, and a closed box is free.
Reconstituted with a preservative-containing diluent: refrigerated, conventionally treated as usable for about 28 days from first entry. Without a preservative, single use and discard.
Two-to-eight-degree refrigeration and minus-twenty freezing are the standard storage conditions for lyophilised peptides in supplier documentation across the market.
The caveat is that storage conditions preserve what you have and cannot improve it.
Dry, cold, dark, still. Four words and you have the answer.