Accepted answer
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.
The fraction of your main peak that is actually your target versus isomers, fragments or related sequences is invisible without complementary identity testing.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
The limitation is that single-digit micro-impurities become invisible at typical reporting thresholds, so "no impurities detected" means "none above one in two thousand."
If you are ranking vendors, specify a method and have all samples tested at the same place.