Accepted answer
More usefully, the single most important distinction is between what purity measures — the fraction of detected material that is your target — and what you actually want to know — how much of the material in the vial is your target.
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.
Column pore size affects mass transfer — a 100 Angstrom packing on a 5 kDa peptide restricts diffusion, broadening the peak and potentially hiding small impurities in the shoulders.
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.