Mechanically, 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.
In practice, buffer versus acid in the mobile phase changes the ionisation state of basic and acidic residues, shifting retention and selectivity — same vial, potentially different separation.
I would be careful about over-reading a single measurement — treat it as a data point, not as ground truth.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.