Infrared temperature-dependent spectroscopy is a well-known tool to characterize folding/unfolding transitions in peptides and proteins, assuming that the higher the temperature, the higher the unfolded population. The infrared spectra at different temperatures of two β-hairpin peptides (gramicidin S analogues GS6 and GS10) are here reconstructed by means of molecular dynamics (MD) simulations and a theoretical-computational method based on the perturbed matrix method. The calculated temperature-dependent spectra result in good agreement with the experimental available spectra. The same methodology has been then used to reconstruct the spectra corresponding to the pure unfolded and folded states, as defined from the MD simulations, in order to better understand the temperature-dependent spectra and to help the interpretation of the experimental spectra. For example, our results show that in the case of the GS6 peptide the analysis of the temperature-dependent spectra cannot be used to investigate the folding/unfolding kinetics within the usual assumption that the higher the temperature, the higher the probability of the unfolded state.