We simulated the thermoreversible micellization–demicellization process and micellar shuttle of a poly(N-isopropylacrylamide-block-ethylene-oxide) (PNIPAM–PEO) diblock copolymer in a water/ionic-liquid (1-butyl-3-methylimidazolium hexafluorophosphate, [BMIM][PF₆]) system by means of dissipative particle dynamics (DPD). The evolution of diblock copolymer chains (micellization–transfer–demicellization) in both water and the ionic liquid phase by the temperature effect reveals that it is a physical phenomenon, dependent on the solubility and interaction parameters of all chemical species involved in the multicomponent system. With the aid of a Monte Carlo simulation we calculated the Flory–Huggins interaction parameters χ of all the species. At room temperature the PNIPAM–PEO copolymer chains are miscible in the aqueous phase. At a higher temperature of T = 303 K the diblock copolymer shows the formation of micelles (micellization process). The micellar transfer to the ionic liquid phase was observed at T = 333 K. A further increase in temperature provokes the demicellization at T = 346 K. The process is reversible: reversing the temperature now to 333 K, shows the formation of the micelles. A further decrease in temperature makes the micelles go back to the water phase. All the simulation outcomes are qualitatively consistent with the experimental results, demonstrating that the DPD methodology may provide a tool for the investigation and analysis of the micellar transfer process in immiscible environments.