The physical origin of the lower critical solution temperature (LCST) behavior of a variety of fluids, including elastin-like polypeptides (ELPs), has been studied for the past few decades. As is the case for polymer solutions, LCST behavior of ELPs is invariably reported for large systems of molecules and is considered evidence for collective behavior. In contrast, we find evidence for properties changes associated with LCST behavior in a single molecule by performing long atomic-level molecular dynamics simulation on the ELP sequences (Val-Pro-Gly-Val-Gly)n for four different length peptides over a wide range of temperatures. We observe a sharp transition in the number of hydrogen bonds between peptide and water and in the number of water molecules within the first hydration shell as temperature rises; this is used to locate the transition temperature. The dependence of the transition temperatures of ELPs on their lengths agrees well with experiments in that both have the same power law exponents. Our simulations reveal that the tendency for pentamers (VPGVG) in ELPs of all lengths to lose H-bonds with water or to gain H-bonds with themselves as temperature rises is independent of the length of the chain in which they are embedded. Thus, the transition temperature of ELPs in pure water is determined by two factors: the hydrogen bonding tendency of the pentamers and the number of pentamers per ELP. Moreover, the hydrogen bonding tendency of pentamers depends only on their sequences, not on the ELP chain length.