The relevant detail is that the honest answer is that the achievable range of plausible purity figures for a given vial is wider than most people expect.
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, gradient slope controls resolution, and gentler slopes resolve co-eluting impurities into separate peaks — so the better method reports the worse purity number.
The Arrhenius relationship for peptide degradation is the basis of accelerated stability testing and also governs how quickly methods drift with temperature.
The caveat is that purity without identity is only half an answer — a high purity does not mean the peak is actually what you think it is.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.