The experimentally observed LCST response (and corresponding swelling and collapse) of elastin-like polypeptides (ELPs) to the addition of salts displays a rich behavior resulting from a combination of ion-specific screening of these weakly charged polyelectrolytes and direct ion-polymer interaction effects. We developed a minimalistic implicit-solvent CG model that can reproduce and qualitatively explain all the experimentally observed effects. Employing further simplifying assumption, we have developed a mean-field model which provides quantitative agreement with the CG computer simulations. Here, an effective second virial coefficient B 2 represents the quality of ions (strongly vs. weakly hydrated, or 'kosmotropic' vs. 'chaotropic' in classical terms) with respect to their affinity and preferential interaction with the polymer.