Accepted answer
Start from what the detector sees, because that tells you what the number means.
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.
Mechanically, 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 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.