Understanding purity requires separating the chemistry from the method from the reporting convention, and the three are not independent.
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.
Put another way, retention time is sequence-specific and method-specific, so comparing your result to a supplier value using a different method is meaningless without method documentation.
Inter-laboratory studies on identical peptide material routinely find half-a-per-cent to a full-per-cent spreads in reported purity on the same sample.
Worth noting that method standardisation is poor in the research-grade space compared to pharmaceutical work, so identical-looking methods can produce different results.
If you are ranking vendors, specify a method and have all samples tested at the same place.