The part that matters: 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.
Sample solvent strength affects peak shape — if you inject in strong solvent on a gradient starting in weak solvent, the solvent peak can distort your main peak or create a false shoulder.
Proline conformer interconversion kinetics are well-characterised and the half-life is of the same order as the chromatographic peak width at room temperature.
Compare purity within a single laboratory on the same method, never across laboratories.