The aggregation of amyloidogenic peptides in liquid water is studied at various temperatures by replica exchange molecular dynamics (REMD) simulations. The formation of a peptide aggregate upon decreasing the temperature reveals features typical for a first-order demixing phase transition, which is smeared out due to the finite size of the simulation box. Various properties of the ensemble of peptides were used to describe the temperature-induced demixing phase transition, which was found to occur at about 375 K. The hydrational and volumetric properties of the peptides and their aggregates are analyzed.