It helps to be literal here: purity is a method-dependent figure, and that is not a limitation of the measurement, it is a property of what the measurement actually answers.
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.
The fraction of your main peak that is actually your target versus isomers, fragments or related sequences is invisible without complementary identity testing.
The ICH Q3A impurity thresholds and the relevant pharmacopoeial chapters all specify method validation requirements that almost no research-grade certificate claims to meet.
Compare purity within a single laboratory on the same method, never across laboratories.