The conformation of a single elastin-like peptide GVG(VPGVG)(3) in liquid water is studied by computer simulations in the temperature interval between 280 and 440 K. Two main conformational states of the peptide can be distinguished: a rigid conformational state, dominating at low temperatures, and a flexible conformational state, dominating at high temperatures. A temperature-induced transition between these states occurs at about 310 K, rather close to a transition temperature seen in experiments. This transition is accompanied by the thermal breaking of the hydrogen-bonded spanning network of the hydration water via a percolation transition upon heating. This finding indicates that the H-bond clustering structure of the hydration water plays an important role in the conformational stability of biomolecules. A second important observation is the Gaussian distribution of the end-to-end distance in the high-temperature state, which supports the idea of a rubber-like elasticity of the studied elastin-like peptide. Finally our results challenge the idea of the folding of elastin-like peptides upon heating.