We performed all-atom and coarse-grained (CG) molecular dynamics (MD) simulations of lipid bilayers grafted with elastin-like polypeptides (ELPs; [VPGVG](n)). All-atom simulations of a single ELP in water show that ELPs become more collapsed and folded as the temperature increases from 293 up to 353 K, in agreement with experiments. All-atom simulations of lipid bilayers composed of dipalmitoylglycerophosphocholine (DPPC), cholesterol, and fatty acids grafted with ELPs show that ELPs insert into the bilayer and significantly disorder lipids, to an extent that depends on the ELP length over the temperature range 293-323 K. In the bilayer, ELPs are mainly, but not entirely, random coil in character at temperatures between 293 and 315 K and, in contrast to the behavior in water, become increasing random coil and extended in length over the range 315-323 K, over which the bilayer is in the disordered liquid phase. The insertion of ELPs into the lipid-tail region is mediated by the interaction of hydrophobic Pro and Val residues with lipid tails, which become stronger at increased temperature, but the insertion is incomplete because of the interaction between hydrophilic backbones of Gly residues and the lipid headgroups. Longer time CG simulations of the transition from ordered gel to disordered liquid bilayer at 315 K in a liposome are able to capture cholesterol flip-flops between bilayer leaflets, leading to an increase in the number of cholesterols in the inner layer, which helps the bilayer accommodate the reduced membrane curvature resulting from the expansion of the bilayer area driven by the phase transition. Our findings indicate that lipid bilayers can be disrupted more effectively by the stronger hydrophobic interaction of the random coils of ELPs at 315-323 K than by the compact ELPs at 293-310 K, which helps explain the experimental observation that ELP-conjugated liposomes are stable at 310 K, but become unstable and release drugs at 315 K.