The method matters more than the vial, which is why specifying a method buys you far more than changing suppliers does.
Temperature affects the dynamics of molecular conformation, and if a peptide has proline residues that interconvert on the chromatographic timescale, the peak will split or shoulder at low temperature and collapse at high temperature.
The part that matters: sample solvent strength affects peak shape — if you inject in strong solvent on a gradient starting in weak solvent, the solvent peak can distort your main peak or create a false shoulder.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
One qualification: achieving purity above roughly 98 per cent on a 30-residue peptide is fighting the chemistry of synthesis, not the quality of the purification.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.